Algebra II - Function Inverses - 10th grade

Which ordered pair is on the inverse of f(x)? (-4, -2) (-2, -2) (-1, -2)

(-1, -2)

Find the values of a through e that make these two relations inverses of each other. a = b = c = d = e =

-3.8 -2.6 1.7 4.4 1

Use f(x) = 12x and f -1(x) = 2x to solve the problems. f−1(−2) = f(−4) = f(f−1(−2)) =

-4 -2 -2

Assignment

...

Use f(x) = 12x and f -1(x) = 2x to solve the problems. f(2) = f−1(1) = f−1(f(2)) =

1 2 2

The rule that maps each domain value to its range value is f(x) = _________x.

1/2

Find the inverse of each of the given functions. f(x) = 4x − 12 f−1(x) = _______x + _______

1/4 3

The inverse of F(C) = 95 C + 32 is C(F) = _______ F − _______.

5/9 160/9

Select each pair of functions that are inverses of each other.

A and B

Select each graph that shows a function and its inverse.

A and D

Check all that apply. F is a function. F is a one-to-one function. C is a function. C is a one-to-one function.

All of them

Compare your response to the sample response above. What did you include in your explanation? a reference to the horizontal-line test a statement that the function is one-to-one the conclusion that the inverse is a function

All of them

Compare your response to the sample response above. What did you include in your explanation? that Danika needs to find g compose f that g(f(x)) must also equal x that g(f(x)) = -x

All of them

Check the functions whose inverses are also functions.

B and C

The range values of an inverse are the _______ values of the original function.

Domain

Waterloo Park posted the following schedule listing the number of hours an employee works on a given day. Let B(x), T(x), R(x), and S(x) represent the number of hours worked by Bill, Ted, Rufus, and Socrates, respectively, on a given day x. What is the value of the inverse shown below? S -1 (0) = Tuesday Friday Ted Rufus

Friday

Good Luck <3

Good Luck <3

Which graphs are inverses of one another? Graph A and B Graph A and C Graph B and C none of the graphs shown

Graph A and C

Is the inverse of the function shown below also a function? Explain your answer.

If the graph passes the horizontal-line test, then the function is one-to-one. Functions that are one-to-one have inverses that are also functions. Therefore, the inverse is a function.

The formula F(C) = 95 C + 32 calculates the temperature in degrees Fahrenheit, given a temperature in degrees Celsius. You can find an equation for the temperature in degrees Celsius for a given temperature in degrees Fahrenheit by finding the function's _________.

Inverse

Talib is trying to find the inverse of the function to the right. His work appears beneath it. Is his work correct? Explain your answer.

No, they forgot to switch the variables after solving the independent variable.

Danika concludes that the following functions are inverses of each other because f(g(x)) = x. Do you agree with Danika? Explain your reasoning.f(x) = |x|g(x) = -x

She is not correct. She forgot to do g compose f. To verify that functions are inverses of each other, you must also show that g(f(x)) = x. Because g(f(x)) = -x, the functions are not inverses of each other.

If the graph of an inverse passes the _______, you know that the inverse is a function.

Vertical-Line Test

The composition of a function and its inverse is always _______.

X

Is f(x) one-to-one?

Yes

Compare your response to the sample response above. What did your explanation include? the conclusion that the work was incorrect an explanation that Talib did not switch the variables at the start an explanation that Talib did not solve for the variable y

all

Select the equation that is the inverse of the given function. f(x) = x-3/5 f^-1(x) = 5x+15 f^-1(x) = 5x+3 f^-1(x) = 3x-5 f^-1(x) = -5/3x

f^-1(x) = 5x+3

Identify the inverse g(x) of the given relation f(x).f(x) = {(8, 3), (4, 1), (0, -1), (-4, -3)} g(x) = {(-4, -3), (0, -1), (4, 1), (8, 3)} g(x) = {(-8, -3), (-4, 1), (0, 1), (4, 3)} g(x) = {(8, -3), (4, -1), (0, 1), (-4, 3)} g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}

g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}

Choose a true statement. g(x) is not a function because f(x) is not a function. g(x) is not a function because f(x) is not one-to-one. g(x) is a function because f(x) is one-to-one. g(x) is a function because f(x) is not one-to-one.

g(x) is a function because f(x) is one-to-one.

h(x) = 2x-4/3. h^-1(x) = 3x-12/2 h^-1(x) = 3/(2x-4) h^-1(x) = 3x+4/2

h^-1(x) = 3x+4/2

In general, f−1(f(x)) = f(f−1(x)) =

x

Adjust m and b to graph the equations below. The inverse of y = 2x + 2 is y = -1/2x-2 y = -1/2x-1 y = 1/2x-2 y = 1/2x-1

y = 1/2x-1

The graph of an inverse is the reflection of the graph of the function over the line _______.

y=x

f(x) has domain _________, and range _________.

{-4, -2, 0, 2 4} {-2, -1, 0, 1, 2}

The range of the inverse of f(x) is {-4, -2, -1, 0, 1, 2, 4} {-4, -2, 0, 2, 4} {-2, -1, 0, 1, 2}.

{-4, -2, 0, 2, 4}