7.5 inverse functions
- 1. 7.5 inverse functions.notebook January 22, 2013 An Inverse Relation switches input and output values. Input x 2 1 0 1 2 Output y 4 2 0 2 4 Input x Output y 1
- 2. 7.5 inverse functions.notebook January 22, 2013 Functions are Inverse Functions if: f(g(x)) = x and g(f(x)) = x Verify that f(x) = x + 3 and g(x) = x 3 are inverse functions. 2
- 3. 7.5 inverse functions.notebook January 22, 2013 Find the inverse of the function f(x) = 2x + 4. To find an inverse function: 1. Replace f(x) with y 2. Switch x and y 3. Solve for y 4. Replace y with f 1(x) Find the inverse of the function f(x) = 4x 3
- 4. 7.5 inverse functions.notebook January 22, 2013 Horizontal Line Test If no horizontal line intersects the graph of a function f more than once, then the inverse of f is also a function. 4
- 5. 7.5 inverse functions.notebook January 22, 2013 Determine whether the inverse of f(x) = x3 + 1 is a function. Then find the inverse. 5
- 6. 7.5 inverse functions.notebook January 22, 2013 Determine whether the inverse of f(x) = x2, where x ≥ 0, is a function. Graph the inverse. 6