Answers
The domain of the inverse of the function f(x) = 5e^x + 3 is found being all real numbers > 3. Or, we can write this symbolically as: D( f^(-1)(x)) = (3,∞)
What is domain and range of a function?Domain is the set of values for which the given function is defined.
Range is the set of all values which the given function can output.
What is inverse of a function?Suppose that the given function is
[tex]f:X\rightarrow Y[/tex]
Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
[tex]f^{-1}: Y \rightarrow X[/tex]
such that:
[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]
(and vice versa).
It simply means, inverse of 'f' is undo operator, that takes back the effect of 'f'
The domain of the inverse of a function (if it exists) is the range of the function it is inverse of. Similarly range of the inverse of that considered function is the domain of that considered function.
The function given is:
[tex]f(x) = 5e^x + 3[/tex]
The domain of the inverse of this function is this function's range.
Assuming only real values are allowed, for any real number x, we have:
[tex]e^x > 0[/tex]
And therefore, we get:
[tex]5e^x > 0 \: \forall x \in \mathbb R\\5e^x + 3 > 3 \: \forall x \in \mathbb R\\[/tex]
Also, since the function [tex]f(x) = 5e^x + 3[/tex] is strictly monotonically increasing and continuous, it touches all the values as its output from any real number > 3 till any finitely large number.
Thus, its range is (3, ∞) (it is an interval consisting of all the real numbers > 3)
This is the domain of its inverse function.
Thus, the domain of the inverse of the function f(x) = 5e^x + 3 is found being set of all real numbers > 3. Or, we can write this symbolically as: D( f^(-1)(x)) = (3,∞)
Learn more about inverse function here:
https://brainly.com/question/19425567
#SPJ1
Related Questions
A parachutist's speed during a free fall reaches 50 meters per second. What is this speed in feet per second? At this speed, how many
feet will the parachutist fall during 10 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round
your answers.
Speed:
0
Х
5
?
Distance fallen in 10 seconds:
Answers
50m ≅164 ft (3s.f.)
50m/s≅164 ft/s
distance after 20s:
d=164 ft/s ⋅20s
=3280ft
Hope This Helps!
An isosceles trapezoid with bottom base 26.5 decimeters, top base 8.5 decimeters, and height 9 decimeters. Find the area. a. 238.5 dm2 c. 157.5 dm2 b. 257.5 dm2 d. 315 dm2 Please select the best answer from the choices provided A B C
Answers
Answer:
the answers c 157.5
Step-by-step explanation:
on edg 2022
The area of given isosceles trapezoid is c. 157.5 decimeters².
What is an area of a trapezoid?The area of a trapezoid is = (1/2*sum of the two parallel sides *height). The area is the sum of the areas of all its faces.The areas of the base, top, and lateral surfaces i.e all sides of the object. It is measured using different area formulas and measured in square units and then adding all the areas. The surface area of a solid object is a measure of the total area that the surface of the object covers.⇒ (1/2*sum of the two parallel sides *height)
⇒ 1/2*(26.5+8.5)*9
⇒ 157.5 decimeters².
Learn more about the area here:-https://brainly.com/question/25292087
#SPJ2
The difference betneen x ond 4, where 4 is greater than x
Answers
This can be written as,
x - 4 > 10Why?✓ We use the operation of subtraction since the terms used is difference. Difference is the result when you subtract numbers.
✓ The symbol for greater than is >. Therefore, you'll have x - 4 > 10 as an answer.
Select the correct answer.
What is the approximate solution to this equation?
15(3)2+ = 90
=
2log
a = log3
O
210g3
t = log 6
O
log 6
210g3
=
log3
2log 6
Answers
Answer:
C) [tex]x=\frac{\log(6)}{2\log(3)}[/tex]
Step-by-step explanation:
[tex]15(3)^{2x}=90\\\\3^{2x}=6\\\\2x=\log_3(6)\\\\2x=\frac{\log(6)}{\log(3)}\\\\x=\frac{\log(6)}{2\log(3)}[/tex]
Remember to use the change of base formula, which states that [tex]\log_a(b)=\frac{\log(b)}{\log(a)}[/tex] so that everything has the same base of 10
Find the size of the angle marked a and b on the diagram
Answers
Answer:
Step-by-step explanation:
we know that the total angles around the big triangle are 180° so, we know the right angle is 90° and we are told that one of the angles is 52° so just find the last angle by
180 = 90 + 52 + X
180 - 90 - 52 = X
38 = X
b = 38°
a = 52°
Answer:
a = 52°b = 38°Step-by-step explanation:
We know:
Angles in a triangle sum to 180°.
Therefore:
52° + 90° + b = 180°
142° + b = 180° |-142°
b = 38°(look at the picture)
a + b = 90° ⇒ a + 38° = 90° |-38°
a = 52°or
Angles 52° and a, are alternate interior angles. Therefore they are congruent.
a = 52°(64 / 8 + 2 - 10) + (9 x 9 + 19) = 2 points 100 90 99
Answers
Answer:
Answer is 100
Step-by-step explanation:
(64/8+2-10) + (81+19)
(8+2-10) + (81+19)
(10-10) + (100)
(0) + (100)
0+100
100
Let f(x) = 3x + 8 and g(x) = x^2 Find (f.g)(x).
Answers
Answer:
3x^2 +8
Step-by-step explanation:
f.g(x) = f(x^2) = 3(x^2) + 8 = 3x^2 +8
Find the volume of this rectangular pyramid.
Be sure to include the correct unit in your answer.
6 m
7 m
9 m
Answers
Answer:
378 M -small 3 that goes on on top right side of the M.
Step-by-step explanation:
you multiply the 6m x 7m x 9m = 378 m to the 3rd power
X= 1/8 y^2
The directrix of the parabola is
y=-2
x=-2
x= 2
Answers
1 of 9
2.
4
5
6
Solve each addition or subtraction problem with its corresponding answer.
a.
11
b. 6
c. 4
d. 1
e.
1. 3
F=-=-= = = = = = =
2. 6
T +
Elo Elm En = 100
3.
5
4. 10
5.
2
11
Check Answer
Answers
Drag the tiles to the correct boxes to complete the pairs not all tiles will be used.
Answers
Answer:
I will answer them from top to bottom
1. 2A
2. 2A-B
3. 2A+3A
4. 2(A-B)
Step-by-step explanation:
You don't need an explanation. I am just putting this here so my answer does not get taken down.
Maribel was approved for a 7-year private student loan at 6.8% to cover her college costs of $10,900. (Round monthly payment calculations to 2 decimal places.)
Answers
Using it's formula, it is found that her monthly payment for the loan will be of $163.45.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.In this problem, the parameters are given as follows:
P = 10900, r = 0.068, n = 7 x 12 = 84.
Hence:
r/12 = 0.068/12 = 0.005667.
Hence the monthly payment will be given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 10900\frac{0.005667(1 + 0.005667)^{84}}{(1 + 0.005667)^{84} - 1}[/tex]
A = 163.45.
More can be learned about the monthly payment formula at https://brainly.com/question/22846480
#SPJ1
Baby Caden wants to arrange 11 blocks in a row. How many different arrangements can he make?
Answers
Explanation:
Start with 11, and count down until you reach 1. Multiply everything along the way.
11*10*9*8*7*6*5*4*3*2*1 = 39,916,800
Or a shortcut would be to say
11! = 39,916,800
The exclamation mark means factorial. It tells the calculator to follow the instructions mentioned above.
The number 39,916,800 is a little over 39.9 million, or you could say it's a bit smaller than 40 million.
Brainliest to the correct answer, but answer ASAP
ONLY answer if you are 100% sure so don't say "I think" or "It might be"
Answers
Answer:
B
Step-by-step explanation:
[tex] \frac{25}{8} = 3.125[/tex]
π = C/d = 25/8 = 3.125
Write an explicit formula for a_na
n
, the n^{\text{th}}n
th
term of the sequence 40, 33, 26, ...
Answers
The nth term of the Sequence: 40, 33, 26, .... is 47 - 7n.
What is Arithmetic Progression?An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same.
Here, we know nth term of the Arithmetic Sequence is
Aₙ = A + (n - 1)D
where, A is first term and D is common difference
A = 40 and D = 33 - 40 = -7
Now, Aₙ = 40 + (n - 1) (-7)
Aₙ = 40 - 7n + 7
Aₙ = 47 - 7n
Thus, the nth term of the Sequence: 40, 33, 26, .... is 47 - 7n.
Learn more about Arithmetic Progression from:
https://brainly.com/question/24873057
#SPJ1
If we invest $5,000.00 in an investment account paying 1% interest compounded annual, how much
will the account be worth in 14 years?
A(t) = P(1+)".
n
The account in 14 years will be worth $
Answers
Answer:
5747.37
Step-by-step explanation:
5 000 ( 1 + .01) ^14
= 5747.37
In a basketball game, Jacob gets 4/9 of the rebounds and Adam gets 3/8 of the rebounds for their team. What fraction of the rebounds did the rest of the team get?
Answers
Answer:
The fraction of the rebounds the rest of the team get was 13/72 (13 out of the 72 total)
Step-by-step explanation:
Jacob gets 4/9
Adam gets 3/8
Since the given fraction provided doesn't have common denominator we would need to do thos first...
4/9 x 8/8 = 32/72
3/8 x 9/9 = 27/72
combining Adam and Jacob rebounds...
32/72 + 27/72 = 59/72
so the remaining, uncounted rebounds are...
72 - 59 = 13
what is c
5a-b+c= -10
a-3b-c= -4
2a+4b-2c= 12
Answers
Answer:
{5a-b+c=10}
{a-3b-c=-4
[2a+2b-c=6
Step-by-step explanation: so it's 6 hope this helps. Let me know if it helps and give brainliest.
solve for absolute value: 3(r+1)+2>-7
Answers
Answer:
[tex]\huge\boxed{\bf\:r > -4 }[/tex]
Step-by-step explanation:
[tex]3(r+1)+2 > -7[/tex]
Use the distributive property to solve 3 (r + 1).
[tex]3r+3+2 > -7 \\3r + 5 > -7[/tex]
Now, bring 5 to the right hand side of the inequality .
[tex]3r > -7-5 \\3r > -12[/tex]
Divide both sides of the inequality by 3.
[tex]r > \frac{-12}{3} \\\boxed{\bf\:r > -4 }[/tex]
[tex]\rule{150pt}{2pt}[/tex]
Which oylinders have the same volume as the cylinder below? Cheok all that apply, height- 20m and base- 32m:
Answers
Answer:
Picture 3: A cylinder with height of 8 meters and diameter of 40 meters.
Picture 5: A cylinder with height of 128 meters and diameter of 10 meters.
Step-by-step explanation:
-------------------------------------------------------------------------------------------------------------
Given:
Which Cylinders have the same volume as the cylinder below? Cheok all that apply, height- 20m and base- 32m:
Answer choices:
picture 1: 40m and 16
picture 2: 5m and 64
picture 3: 40m and 8
picture 4: 32m and 20
picture 5: 10m and 128
Formula for Cylinders:
V=Bh or V=πr²h
-------------------------------------------------------------------------------------------------------------
Diameter = Half of Radius {Divide by 2}
Original Cylinder:
20m and 32m
20/2 = 10
V=πr2h=π·102·32≈10053.09649
V ≈ 10053.1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Picture 1: 40m and 16
40/2 = 20
V=πr2h=π·202·16≈20106.19298
V ≈20106.19
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
picture 2: 5m and 64
5/2 = 2.5
V=πr2h=π·2.52·64≈1256.63706
V ≈1256.64
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
picture 3: 40m and 8
40/2 = 20
V=πr2h=π·202·8≈10053.09649
V≈10053.1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
picture 4: 32m and 20
32/2 = 16
V=πr2h=π·162·20≈16084.95439
V≈16084.95
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
picture 5: 10m and 128
10/2 = 5
V=πr2h=π·52·128≈10053.09649
V≈10053.1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
After solving each answer choices the answers are:
picture 3: 40m and 8
picture 5: 10m and 128
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Kavinsky
1 × 10^ − 4 ) + ( 2 × 10^ − 2 )
Answers
Answer:
[tex]2.01 *10^{-2}[/tex]
Step-by-step explanation:
this is the correct answer
Write the equation of the circle graphed below.
Answers
Answer:
Your equation is [tex](x - 1)^2 + (y +1)^2 = (\frac{1}{2} )^2[/tex]
Step-by-step explanation:
Well, the center origin of the circle is given (h,k) = (1,-1).
We have to find our radius as they gave us a point. from origin to the edge of the circle.
Using the formula: (x - h)^2 + (y - k)^2 = r^2
Plug in our (h,k) = (1,-1) and (x,y) = (0.5,-1) to solve for radius.
(x - h)^2 + (y - k)^2 = r^2
(0.5 - (1))^2 + (-1 - (-1))^2 = r^2
(-0.5)^2 + (0)^2 = r^2
1/4= r^2
r^2 = 1/4
r = 1/2
Consider the
equation
S=Ut+ 2gt²
Answers
The formula s= ut + 1/2gt^2
Represents the total distance "s" travelled by an object in time "t" which has an initial speed of "u" and is accelerating at the uniform rate of "g". It is customary to use the symbol "g" for acceleration due to gravity. However this equation is valid for any value of uniform acceleration.
We can derive the equation as follows.
The total distance travelled by a uniformly accelerating object is equal to average speed multiplied by time
That is: s = (average speed)*t ... (1)
And, average speed = (initial speed + final speed at the end of period t)/2
And final speed = u + gt
Therefore: Average speed = (u + u + gt) = 2u + gt
Substituting this value of average speed in equation (1) we get:
s = (2u + gt)/2]*t = ut +1/2gt^2
hope it helps...!!!
QUESTION ON PIC THANK YOU
Answers
Answer:
10/10
Step-by-step explanation:
What is the least common multiple of 2 and 5
Answers
Answer:
10Step-by-step explanation:
We Notice that 2 and 5 are two prime numbers
Remark : the least common multiple of two prime numbers is equal to their product .
Then
LCM(2 , 5) = 2 × 5 = 10
2 * 5
= 10 ⟶ least common multiple of the number (since no common factor is there)
Imad and Amra are butterflies. Imad drinks 3 grams of nectar a week. Amra drinks 2 grams of nectar a week. How many grams of nectar do they drink all together after 4 weeks?
Answers
Answer:
20 grams
Step-by-step explanation:
3+2=5 grams for 1 week
5x4=20
Simplify the expression 3(7x).
help
Answers
Answer:
21x
Step-by-step explanation:
7x is one term. With parenthesis, you have to multiply whatever is on the outside, inside. So that's 3*7x, or 21x.
Hope this helps!
Hey there!
3(7x)
= 3 * 7x
= 7x * 3
= 7x + 7x + 7x
= 14x + 7x
= 21x
Therefore, the answer should be: 21x
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Identify the maximum or minimum value, domain, and range of the graph of the quadratic function.
Answers
Answer:
See below ~
Step-by-step explanation:
Details of the graph
Maximum = 4 [highest value past which no values are part of the graph]Domain : all real numbers [graph is vertical, so it will be all possible real numbers]Range : y ≤ 4 [all y values are less than or equal to 4 according to the graph]simplify the ratio of 1:3¼
Answers
Answer:
[tex]\frac{4}{13}[/tex]
Step-by-step explanation:
1÷3[tex]\frac{1}{4}[/tex]=3+[tex]\frac{1}{4}[/tex], 3×[tex]\frac{4}{4}[/tex]
1÷[tex]\frac{13}{4}[/tex]
Elly is a self-employed financial advisor. Last year her income was $57,000.How much does she owe in SECA taxes?
Answers
The SECA taxes for the income $57000 will be $7068.
What is SECA?SECA stands for Self Employed Contributions Act. These taxes are computed from the net earnings, which in this case is $57000.
The basic rate for SECA taxes is 6.2% for employeer and 6.2% for employee. In the case of people who are self employed, the taxes are double, because they are employee and employeer at the same time.
So, Doug have to pay 12.4% taxes, which is equivalent to:
[tex]\rm SECA=57000\times 12.4\%= $7067[/tex]
Therefore, the SECA deduction for Doug is $7068.
To know more about SECA follow
https://brainly.com/question/19499340
#SPj1
