Functions

Inverse Functions

1. If a graph passes a vertical line test,

then it is a

RememberAim: Exchange the y and x variables in an equation in order to reflect an image through the y = x line.

2. Solve the following for y: 2y + 3 = x

3. Which transformation is illustrated below?

2y = x - 3

y = x – 3 2

reflection

function

Inverse Functions

Aim: Exchange the y and x variables in an equation in order to reflect an image through the y = x line.

When a function receives input, it generates output.

What if we have the output, and would like to find the input of the a function?

In other words, how can we undo a function?

switch the x and y

Algebra

get into y = form

Find the inverse function of f(x) = 3x - 2

change f(x) to y

change y to f -1(x)

Aim: Exchange the y and x variables in an equation in order to reflect an image through the y = x line.

You have found the inverse if it passes the horizontal line test.

Graph

Graph the inverse function of f(x) = 3x - 2 f-1(x) = x + 2

3

Aim: Exchange the y and x variables in an equation in order to reflect an image through the y = x line.

= 1 x + 2 3 3

Notice the reflection.

Try this …

Find the inverse function of f(x) = x2

y = x2

x = y2√ √±√x = y

f -1(x) = ±√x

Aim: Exchange the y and x variables in an equation in order to reflect an image through the y = x line.