Objectives: To find inverse functions graphically & algebraically.

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Presentation transcript:

Objectives: To find inverse functions graphically & algebraically.

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

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

Show that f and g are inverse functions. Ex2

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…

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.

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

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

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)

Ex 6 Find the inverse of each function A B

Ex 7 Find the inverse of each function A B