4.2 Inverse Functions There are only four words in the English language that end in “-dous”. Name one.

4.2 Inverse Functions There are only four words in the English language that end in “-dous”. Name one. Tremendous Horrendous Stupendous Hazardous

One-to-One A function is one-to-one if for each y value there is only one corresponding x value. Otherwise, it is many-to-one. many-to-one one-to-one Horizontal Line Test: If a horizontal line intersects the graph of a function f in only one point, then f is one-to-one.

Inverses Let f denote a one-to-one function. The inverse is denoted f -1(x) and Verify that f and g are inverses of one another.

Graphs of Inverse Functions The graph of a function f and its inverse f -1 are symmetric with respect to the line y = x.

Finding Inverses Domain Range Domain Range The domain of f is equal to the range of f -1 and vice versa.

Finding Inverses Find the inverse of where .

Finding Inverses Find the inverse of where .

Using Inverses to Find Range Find the inverse of . Then find the range of f using f -1.

4.2 Inverse Functions Homework #13: pgs. 267 #9 – 19 odd, 27 – 41 odd, 59 – 67 EOO