6.4 Notes – Use Inverse Functions. Inverse: Flips the domain and range values Reflects the graph in y = x line. Functions f and g are inverses of each.

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6.4 Notes – Use Inverse Functions

Inverse: Flips the domain and range values Reflects the graph in y = x line. Functions f and g are inverses of each other if f(g(x)) = x and g(f(x)) = x Notation: f(x) -1 is the inverse of f(x)

1. Find an equation for the inverse relation. y = –2x + 5 x = –2y + 5 –5 x –5 = –2y –2

2. Find an equation for the inverse relation. –2 3x – 2 = –2y –2 3 3x = –2y + 2

3. Verify that f and g are inverse functions. f(g(x)) = x

3. Verify that f and g are inverse functions. f(g(x)) = x g(f(x)) = x

4. Verify that f and g are inverse functions. f(g(x)) = x

4. Verify that f and g are inverse functions. f(g(x)) = x g(f(x)) = x

Graph the function f. Then graph the inverse on the same graph. Is the inverse a function? 5. Inverse: +6 x + 6 = 3y 3 3 Yes, the inverse is a function

Graph the function f. Then graph the inverse on the same graph. Is the inverse a function? 6. No, the inverse is a NOT a function x y x = –b2a–b2a = –(0) 2(1) = –1 –2 –3 –2 1 1 x y –1 –2 –3 –2 1 1 inverse