1. DO NOW: Perform the indicated operation.
1.) Find g(f(x)) if f(x) = 2x2 – x and
g(x) =
2.) Find g(h(8)) if g(x) = -x2 and
h(x) =

2. Algebra II
5.6: Inverse of a Function

3. Exploring Inverses
Inverse functions interchange input and output values.
The domain and range are also interchanged
The graph of an inverse function is a reflection of the graph of the original function.
The line of reflection is y = x

4. Exploring Inverses.
To find the inverse of a function algebraically, switch the roles of x and y.
Then solve for y.

5. Example 1
Find the inverse of f (x ) = 3x − 1.

6. Inverses of Nonlinear Functions
In the previous examples, the inverses of the linear functions were also functions.
However, this may not always be the case.

7. Sketch the graph of the inverse relation. Are these inverse functions?

8. Example 2 Find the inverse of
f (x ) = x 2, x ≥ 0. Then graph the function and its inverse.

10. Example 3
Consider the function f (x ) = 2x Determine whether the inverse of f is a function (you may use your graphing calculator). Then find the inverse.

11. Do Now: Solve the literal equation for x.
1. y  3x − 9x a  x − 7xz
3. sx − tx  r C  86x − 59

12. Example 4

13. Exploring Inverse Functions
Functions f and g are inverses of each other provided:
f(g(x)) = x and g(f(x)) = x

14. Example 5

15. Practice