Inverse functions

Does every function have an inverse?

No. A function must be 1 to 1 , or pass the horizontal line test in order to have an inverse.

PASS FAIL

Notation: or 1f )(1 xf

Characteristics of an inverse function

• Algebraically

– The domains and ranges are switched

• Graphically

– The graphs are reflections across the line y = x

21

21

yx

xy

How to find an inverse function

1. Verify it passes the HORIZONTAL line test

2. Replace f(x) with y.

3. Switch x and y

4. Solve for y

Example:

Show that and

are inverses a) algebraically b ) graphically

15)( xxf 5

1)(

xxg