1. Objectives: To find inverse functions graphically & algebraically.

2. Inverse Function
Let f & g be two functions. The function g is the inverse function of f if:
f(g(x)) = x for every x in the domain of g
and
g(f(x)) = x for every x in the domain of f
Notation for the Inverse function of f is

3. Ex 1. Which of the functions is the inverse of .

4. Show that f and g are inverse functions.
Ex2

5. Algebraically… Graphically…
Switch x & y variables to find new equation.
Graphs are reflections of each other in the line y = x.
Switch coordinates of f(x).
Graphically…

6. Ex 3. Sketch the inverse of f
Ex 3. Sketch the inverse of f. Use the horizontal line test to determine whether the inverse is a function.

7. Sketch the graph and its inverse
Is the inverse a function?

8. Ex4: Does the function have an inverse?
If so, find it. X
F(x) -3 10 -2 6 -1 4 1 2 3 X
F(x) -3 10 -2 6 -1 4 1 2 3
-10

9. Ex 5. Find the inverse function of f algebraically.
Step 1: Write original function.
Step 2: Replace f(x) by y.
Step 3: Interchange x & y.
Step 4: Isolate y.
Step 5: Replace y by f -1(x)

10. Ex 6 Find the inverse of each function
A B

11. Ex 7 Find the inverse of each function
A B