1. 4-5:One-to-One Functions and Their Inverses
A function is f(x). An inverse function, f-1(x) undoes the function. The domain of the original function is the range of the inverse and vice versa. The graph of the inverse of a function is the mirror image of the function’s graph over the line y=x. The latter is the line of symmetry between a function and its inverse.

2. The inverse of a function is NOT always a function
The inverse of a function is NOT always a function. A function is considered one-to-one if the inverse is also a function. Use the vertical line test to determine if the original graph is a function. Use the horizontal line test to determine if the inverse will be a function.

3. Finding an inverse algebraically: Given some function f(x). 1
Finding an inverse algebraically: Given some function f(x). 1.) Switch the x and y parts. 2.) Solve the new equation in terms of y. 3.) Write the new equation as f-1(x). Determine algebraically if two functions are inverses. Use composition. If f(g(x))=g(f(x))=x, then the functions are inverses of each other.

4. Some notations Suppose a function f has an inverse
Some notations Suppose a function f has an inverse. If f(2)=3, find each of the following: f-1(3)=? f(f-1(3))=? f-1(f(2))=?

5. Determine whether the function is one-to-one.

6. Determine whether the function is one-to-one.

7. Determine whether the function is one-to-one.

8. Determine whether the function is one-to-one.

9. Function Inverses

10. Function Inverses

11. Function Inverses

12. Function Inverses