Inverse functions

What does it mean to find the inverse of f(x) ?

To find f ^-1(x)

What is the first step to find f^-1(x) ?

Switch the places of x and y

Answer

f^-1(x) = 1/x-1

f^-1(x) = 7x/ 3(x-1)

f^-1(x) = 5x/4x-2 or f^-1(x) = 5x/2(2x-1)

f^-1(x) = - 9x/x-4

f^-1(x) = 9/2x

f^-1(x) = x-7/5

f^-1(x) = 7/8x

How do you find the inverse of a function on a graph?

reflect it over the line y = x

You cannot cancel out a variable if….

if it is next to another variable.

f(x) is the same as…

Y

Remember the first step in the equation if it has a radical is to ____ ___ __ ______ because the answer _____ ____ _ ______.

take out the radical, cannot have a radical

Finding the inverse of f^-1(x) basically means to find…

Y. get Y by itself.

Factor 30x + 3x

3(10 + x)

Factor: 3(x + 2) - 7x(x + 2)

(3 - 7x)(x + 2)

Find the inverse of the function:

y = 2ײ + 3

f⁻¹(x) = ± √x−3/2​

Find the f^-1(x) of the function:

F(x) = x/x + 3

f^-1(x) = -3/x - 1

Find the inverse of f(x) = √x + 2

x² - 2 = y

What does inverse mean?

Opposite

What is the term representing the inverse of something?

f^-1(x)

How do you find the inverse of a function on a graph?

Reflect the function over y = x

What is the first step in solving a inverse function?

Switch the y and x (domain and range)

X represents the _____ of a function

domain

Y represents the _____ of a function

range

Remember: There is always a _____ ___ being multiplied with x.

invisible one

Remember: Everything is always _____ by ___.

divided by one.

What is a different way of representing x/2 ?

½ x (Remember, x can be replaced/is always multiplied by 1.

Solve for x:

y = 2x + 5

x = (y - 5)/2

Factor: 40 + 40x

40(1 + x)

When are trying to find the inverse of f(x) what are you solving for?

y, f^-1(x)

When are trying to find the inverse of f^-1(x) what are you solving for?

x,f(x)

What is the inverse of the function y = 4x + 5?

(x/4) - (5/4) = y, or just (x-5)/4 = y

Find f^-1(x) of the function:

f(x) = ³√(x + 2)

x³ - 2 = y

If f(x) = 12x + 4, then what is the inverse function?

f^-1(x) = (x/12) - (1/3) = y

Find the inverse of f(x) = √(x + 2)

f^-1(x) = x² - 2

What is the inverse of f(x) = x³ - 2

f^-1(x) = ³√(x + 2)

For the function f(x) = (x - 3)³ + 1, find f^-1(x).

³√(x - 1) + 3 = y

If f(x) = ³√(x) + 4, then f^-1(x) equals

f^-1(x) = (x - 4)³

The inverse of the function f(x) = (x + 1)/(x - 2) is…

f^-1(x) = (2x + 1) / (x - 1)

f(x) = x³ - 3

Given f^-1(x) = ³√(x - 3b) what is the only possible value for b?

b = -1

Write an equation for the inverse of f(x) = (x + 2) / 8

f^-1(x) = 8x - 2

If f(x) = (1/2)x + 2 , then the inverse function f^-1(x) is…

f^-1(x) = 2x - 4

Given f^-1(x) = -(3/4)x + 2, than what is f(x) ?

f(x) = -(4/3)x + (8/3)