6.4 “Inverse Functions”

6.4 “Inverse Functions” A relation is a pairing of input and output values. An inverserelation means that the domain and range are interchanged. The graph of an inverse is a reflection of the original graph Functions f and g are inverses of each other if….. f(g(x)) = x andg(f(x)) = x The function g is written as f-1(x), which is the inverse.

Finding Equations of Inverses 1. Find an equation for the inverse of y = 3x - 5 Steps: 1. Write the original problem. • Switch x and y. • Solve for y. • This is the inverse function.

Verifying Inverse Functions 2. Verify that f(x) = 3x – 5 and f-1(x) = x + are inverse functions.

Try These 1. Find the inverse of the function y = 4x + 2 2. Verify they are inverses.

Inverses of Nonlinear Functions • Find the inverse of f(x) = x2, x ≥ 0. Then graph f(x) and f-1(x).

Inverses of Nonlinear Functions 4. Consider the inverse of f(x) = 2x3 + 1. Determine whether the inverse of f is a function.

Try This… 5. Find the inverse of f(x) = x2 + 2, x ≥ 0. Then graph f(x) and f-1(x).

Try This Too  6. Consider the inverse of f(x) = 3x3– 4. Determine whether the inverse of f is a function.

Horizontal Line Test Use the horizontal line test to see if inverses are functions. No horizontal line intersects the inverse more than once!

6.4 “Inverse Functions”