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.
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