Answers
f(x) = 1/(1 - x)
g(x) = (x - 1)/x
The inverse functions f ⁻¹(x) and g ⁻¹(x), if they exist, are such that
f( f ⁻¹(x) ) = x
g( g ⁻¹(x) ) = x
So we have
f( f ⁻¹(x) ) = 1/(1 - f ⁻¹(x) ) = x
Solve for f ⁻¹(x) :
1 = (1 - f ⁻¹(x) ) x
1 - f ⁻¹(x) = 1/x
f ⁻¹(x) = 1 - 1/x
f ⁻¹(x) = (x - 1)/x
and so f ⁻¹(x) = g(x).
Similarly, you can solve for g ⁻¹(x) :
g( g ⁻¹(x) ) = (g ⁻¹(x) - 1) / g ⁻¹(x) = x
1 - 1/g ⁻¹(x) = x
1/g ⁻¹(x) = 1 - x
g ⁻¹(x) = 1/(1 - x)
So we know f(x) and g(x) are inverses of one another,
f ⁻¹(x) = g(x)
g ⁻¹(x) = f(x)
Then
(a) (f o g)(x) = x
(b) (g o f ⁻¹)(x) = g(g(x)) = (g(x) - 1)/g(x) = 1 - 1/g(x) = 1 - x/(x - 1) = 1/(1 - x)
(c) (f o g ⁻¹)(x) = f(f(x)) = 1/(1 - f(x) ) = 1/(1 - 1/(1 - x)) = 1/(x/(x - 1)) = (x - 1)/x
Related Questions
Mrs. Applebaum goes to the supermarket to buy a box of cereal. She has a coupon for 35 cents off. The original
price is $4.73. How much does she need to pay for the cereal?
O $1.23
O $4.38
$4.48
O $5.08
HELPP
Answers
Answer:
4.73 - 0.35 = 4.38. Mrs Applebaum needs to pay $4.38
Step-by-step explanation:
Answer:
$4.38
Step-by-step explanation:
$4.73 is the full price. She has a coupon for 35 cents OFF which means you have to subtract .35 from 4.73. 4.73 - .35 = 4.38
-170=-7(8n-7)+5 please help
Answers
Answer:
n=4
Step-by-step explanation:
Let's get rid of the parenthesis first. We're left with -170=-56n+49+5. Let's move all of the numbers together so that the variable is separated from the numbers. Now we have 56n=224 using inverse operations. If we divide both sides by 56, we're left with n=4.
Hope this helped!
Answer:
n = 4
Step-by-step explanation:
-170=-7(8n-7) +5
-170=-56n+49+5
-170=-56n+54
-170+56n=54
56n=170+54
56n= 224
n=4
What does 2x+1=3x-4 equal?
Answers
Answer:
5
Step-by-step explanation:
2x + 1 = 3x - 4
-2x -2x
--------------------
1 = x - 4
+4 +4
----------------
5 = x
The answer is 5.
Hope this helped.
what is the area of the figure below?
Answers
Answer:
D. 72 [tex]in^2[/tex]
Step-by-step explanation:
The square is 36 in2
The 2 triangles are both 18 in2.
36+18+18=72 in2
I hope this helps!
pls ❤ and give brainliest pls
Answer:
Area is 72 in²
Step-by-step explanation:
= Area of three triangles + area of square.
[tex]{ \bf{ = 3 \times ( \frac{1}{2} b \times h) + (s \times s)}}[/tex]
substitute:
[tex]{ \sf{ = ( \frac{1}{2} \times 6 \times 6) + 2( \frac{1}{2} \times 6 \times 3) + (6 \times 6)}} \\ = { \sf{18 + 18 + 36}} \\ = { \sf{ {72 \: in}^{2} }}[/tex]
math is a bummer bro
Answers
Answer:
alr let's start
one clock 12 hrs => 360 °
so 1hr=> 30°
now visualise clock with struck 8
between 12 and 8 from smaller angle we get that there are 4 hrs in between so
4 × 30 = 120°
done Dana done done
Answer:
ANGLE=120°
SEE THE IMAGE FOR SOLUTION
Chapter 9-4 composition of isometrics (anyone pls help me TwT)
Answers
Both answers are "translation" which is the same as up/down/left/right shifting.
Refer to the diagram below to see how the reflections combine to form this shifting. A composition of two reflections always leads to a translation whenever the mirror lines are parallel. The direction of the shifting is perpendicular to the parallel lines. If the mirror lines intersected, then we'd have a rotation instead.
I used GeoGebra to create the diagram.
PLEASE HELP ME I WILL MARK BRAINLIEST!
Answers
compute the range of the figures into the table
Condition for increasing decreasing and concavity of function
Answers
Answer:
If the concavity of f changes at a point (c,f(c)), then f′ is changing from increasing to decreasing (or, decreasing to increasing) at x=c. That means that the sign of f″ is changing from positive to negative (or, negative to positive) at x=c. This leads to the following theorem
Step-by-step explanation:
The previous section showed how the first derivative of a function, f′ , can relay important information about f . We now apply the same technique to f′ itself, and learn what this tells us about f . The key to studying f′ is to consider its derivative, namely f′′ , which is the second derivative of f . When f′′>0 , f′ is increasing. When f′′<0 , f′ is decreasing. f′ has relative maxima and minima where f′′=0 or is undefined. This section explores how knowing information about f′′
Let f be differentiable on an interval I . The graph of f is concave up on I if f′ is increasing. The graph of f is concave down on I if f′ is decreasing. If f′ is constant then the graph of f is said to have no concavity.
Note: We often state that " f is concave up" instead of "the graph of f is concave up" for simplicity.
The graph of a function f is concave up when f′ is increasing. That means as one looks at a concave up graph from left to right, the slopes of the tangent lines will be increasing. Consider Figure 3.4.1 , where a concave up graph is shown along with some tangent lines. Notice how the tangent line on the left is steep, downward, corresponding to a small value of f′ . On the right, the tangent line is steep, upward, corresponding to a large value of f′ .
PLEASE HELP ASAP :))
Sophie tried to evaluate an expression. Here is her work:
92 : 32.2 + 7.6
= 81 - 9.2 + 7.6
Step 1
= 9.2 + 7.6
Step 2
= 18 + 7.6
Step 3
= 25.7
Step 4
= 175
Step 5
Is Sophie's work correct?
Yes, Sophie's work is correct
No, Sophie made a mistake going from Step 1 to Step 2
O No, Sophie made a mistake going from Step 3 to Step 4.
No, Sophie made a mistake going from Step 2 to Step 3
Answers
Explanation:
Using PEMDAS, or the order of operations, Sophie should have finished multiplying before adding. Here’s how her expression should’ve ended:
= 18 + 7 • 6
= 18 + 42
= 60
In the diagram below, PQ is parallel to MN. Solve for 2. Round your answer to the
nearest tenth if necessary.
X=
Answers
Michelle gets10rewards points for each of her purchases at Starbucks. With 500 rewards points, she can get a free smoothie. If she has 370 points saved, how many purchases will it take her to get her free smoothie?
Answers
she needs 130 points saved up
Answer:
13
Step-by-step explanation:
1.11(5) - 11(4) =
2.8(-3 + 2) =
3.6(9) - 4(6) =
4.7(4) - 2(0) =
5.15(3) - 2(12) =
6.9(5 + 3) =
7.12(2) - 7(2) =
8. 8(3) =
9.(6)6) =
10.11(9) =
11.8(5) - 2(7) =
12.5(n) =
13.5y(2) =
14.13(x + 2) =
15. 16(5x - 8) =
16.23y( 2 + 4) =
Answers
Answer:
1) 11
2) -8
3) 30
15) 80x - 128
16) 138y
Step-by-step explanation:
For these problems, you will need to use either PEMDAS or distributive property.
PEMDAS stands for parentheses, exponents, multiplication/division, addition/subtraction. Problems must be solved by going in order of the acronym, always starting with anything in parentheses first.
Example of PEMDAS:
2) 8(-3 + 2)
Solve for what's inside the parentheses first. There are no exponents, multiplication, or division within the parentheses so next would be addition and subtraction.
-3 + 2 = -1 so the problem will now look like:
8 (-1)
Next, PEMDAS says to look for exponents. There are none. Multiplication and division are next. 8 is being multiplied by -1 so lets try that:
8 × -1 = -8
-8
Distributive property is when you take the number being multiplied on the outside of the parentheses and multiply it to each individual number within the parentheses.
Example of distributive property:
2) 8(-3 + 2)
Multiply the number on the outside of the parentheses, 8, to each number within the parentheses, -3 and 2:
8 × -3 and 8 × 2
The problem should look like:
-24 + 16
Then solve:
-8
Use whichever method you are most comfortable with as both will produce the same answer. I will solve the first few and the last few to help you.
1)
11(5) - 11(4)
55 - 44
11
3)
6(9) - 4(6)
54 - 24
30
15) *You must use distributive property for these last problems as you cannot add or subtract numbers and variables*
16(5x - 8)
80x - 128
*You can only combine like terms so this is fully simplified*
16)
23y(2 + 4)
46y + 92y
138y
PLEASE HELP I WILL MARK YOU BRAINLIEST IF CORRECT
Answers
Sure, I will help you. The answer you are looking for is x=11.
Solution/Explanation:
Write out the equation:
3(x+5)=5x-7
Using the Distributive Property on the LEFT SIDE,
3x+15=5x-7
Next, subtracting 3x from both sides,
3x-3x+15=5x-3x-7
15=2x-7, or 2x-7=15
2x-7=15
Now, adding seven to both sides,
2x-7+7=15+7
2x=22
Finally, dividing both sides by 2,
So, therefore the final answer is x=11. And, also, the next step would be written as 3x+15=5x-7, as stated above, preliminarily.
I hope this helped you find your answer. Enjoy your day, and take care!
The answer you are looking for is 3x+15=5x-7. But, the answer is x=11.
The formula for the circumference of a circle is c= 2pi r, where r is the radius. Rearrange the formula to solve for our and select the correct option below
Answers
Answer: r = C/(2pi)
This is the same as writing [tex]r = \frac{C}{2\pi}[/tex]
=========================================================
Explanation:
pi is some number (approximately 3.14) which means 2pi is also some number (roughly 6.28)
Saying c = 2pi*r means we have 2pi times r, and the result is the circumference c. To isolate r, we'll undo the multiplication. We'll undo it by dividing both sides by 2pi like so
C = 2pi*r
C/(2pi) = r
r = C/(2pi)
in which we can write it like [tex]r = \frac{C}{2\pi}[/tex]
So whatever C is, we divide it over 2pi (aka roughly 6.28) to get the radius.
-----------------
Extra Info (Optional Section):
As an example, let's say the circumference of the circle is 628 feet. This means the distance around the circle is 628 feet. So C = 628 would lead to...
r = C/(2pi)
r = C/(6.28)
r = 628/(6.28)
r = 100
So the radius would be roughly 100 feet.
Ralph owns the farmer’s silo shown. The silo is a cylinder with a half-sphere as the roof. He wants to fill it up with corn for the pigs. If it costs $1.13 per cubic meter to purchase the corn, how much will it cost to fill up the whole silo?
Answers
Answer:
Half-Sphere Volume = [( π •diam³) / 6] / 2
Cylinder Volume = ¼ • π • diam² • height
Cylinder height = 19 meters
Sphere diameter = 10 meters
Cylinder portion = ¼ • π • diam² • height
Cylinder portion volume = ¼ • π • 10² • 19
Cylinder portion volume = 1,492.26
Half-Sphere Volume = [( PI * 10^3) /6 ] / 2
Half-Sphere Volume = 261.80
Total Volume = 1,492.26 + 261.80 = 1,754.06 cubic meters
corn is $1.13 per cubic meter
total cost = 1,754.06 * $1.13 = 1,982.08
Answer is C 1,981.08
Step-by-step explanation:
Can anyone help me with this question?
x^{2} + 7x -144
quadratic equations
Answers
Answer:
?
Step-by-step explanation:
Brainly challenge.
if the cost of 2:dozen copies is Rs 720 , find the cost of 72 copies .
Answers
Answer:
Rs 2160
Step-by-step explanation:
1 dozen = 12 copies
2 dozen = 24 copies ( 2*12)
72÷12 = 6 dozen
72 copies = 6 dozen
1 dozen = Rs 720÷2
1 dozen Rs 360
6 dozen = 360*6
6 dozen = 72 copies = Rs 2160
I need help finding y
Answers
to solve for y, we must multiply by t on both side to get ride of the t in the denominator. By doing this, we will get:
[tex] {t}^{3} [/tex]
on the right side.
Subtracting 3, and we have successfully isolated y.
It would be impossible to get a quantitative value for y if we don't know the value of t.
respuesta listsdafddfssdffd
Given the function g(x) = x2 + 10x + 18, determine the average rate of change of
the function over the interval -11 < x < -1.
Answers
Answer:
-2.
Step-by-step explanation:
Average rate of change of the function = [ f(-1) - f(-11)] / [(-1 - (-11)]
= [(-1)^2 + 10*-1 + 18 - ((-11)^2 + 10*-11 + 18)] / 10
= (1 - 10 + 18 - (121 - 110 + 18) / 10
= (9 - (29) /10
= -20/10
= -2.
Answer:
Step-by-step explanation:
The answer is +2 or 2.
30 in.
20 in.
36 in.
Find the area of the trapezoid shown above.
[?] square inches
Answers
Answer:
660 in^2
Step-by-step explanation:
The formula to calculate area of trapezoid : (a+b)/2*h (a: base, b: base, h: height)
(30+36)/2*20 = 660 in^2
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Answers
Step-by-step explanation:
tujh vitamin ve j hhhjuhhujuhhggggggggggggAnswer:
The answer is C 93.6
Step-by-step explanation:
The volume of a triangular prism: [tex](\frac{base*height}{2} ) * height of the prism[/tex]
so
[tex]\frac{(8)*(3.9)}{2} *4 = 93.6[/tex]
8. PLEASE HELPP!! Find the area of the shaded sector. Leave your answer in terms of .
Answers
Answer:
Area of a complete circle = PI * r^2
The shaded area is 1/3 of the circle so
Area = (PI * 9^2) / 3
Area = (254.4690049408) / 3
Area = 84.8230016469
Area = 84.82 square feet (rounded)
Step-by-step explanation:
can you please tell me the answer I don't know
Answers
Answer:
Twenty-eight billion five hundred forty-two million rupees
28,542,000,000 rupess
or, 28.542 × 10⁹ rupees
(2) Mele scored 70% on
a fun
geography quiz. What fraction of the
test did she get right?
Answers
Type the correct answer in each box. Use numerals instead of words,
Cassie's age is 3 less than twice Kara's age. The sum of their ages is 42.
Create an equation to find Kara's age, n.
nt(
[
70
Answers
Answer: x + 2x - 3 = 42 is the equation and kara is 15 years old and cassies is 27 years old.
Step-by-step explanation:
Let age of kara be x years
Cassie's age will be 2x-3 years
ATQ
x + 2x-3 = 42
3x = 42+3
3x = 45
x = 45/3
x = 15
Kara's age = 15 years
Cassie's age = (15×2)-3
= 30-3
= 27 years
please click thanks and mark brainliest if you like :)
Answer:
Step-by-step explanation:
Answer always, sometimes or Never.
Natural numbers are ----------- integers
Irrational numbers are ----------- rational numbers
Rational numbers are --------- real numbers
Square roots are __________Rational numbers
Answers
Step-by-step explanation:
1)Always
2)never
3)Always
4)Never
[tex]\frac{1}{5} x + \frac{4}{5} = \frac{8}{5}[/tex]
Answers
Answer:
x = 4
Step-by-step explanation:
1/5x + 4/5 = 8/5
Multiply each side by 5 to get rid of the fractions
5(1/5x + 4/5) = 8/5 *5
x+4 = 8
Subtract 4 from each side
x+4-4 = 8-4
x = 4
Jimmy is saving money to buy a concert ticket for $155. He has $42 so far and he can save $20 per week. In how many weeks will he have enough money to buy the ticket? Select an equation that could be used to answer the question above. Let W represent the number of weeks. A. 20w + 42 = 155 B. 20w - 155 =42 C. 42w + 20 = 155 D. 155w - 20 = 42
Answers
Answer:
The answer for this question is A
What is the quotient when the polynomial 4x2 - 2x - 12 is divided by 2x - 4?
Answers
which of the following is a quotient of the rational expressions shown here?
Answers
Answer:
x^2+x
--------
x-1
Step-by-step explanation:
x 1
------ ÷ --------
x-1 x+1
Copy dot flip
x x+ 1
------ * --------
x-1 1
x(x+1)
-------
x-1
x^2+x
--------
x-1
