2.  If f is a one-to-one function with domain D and range R, then the inverse function of f, denoted f -1, is the function with domain R and range D defined by f -1 (b) = a if and only if f(a) = b

3. Injective, Surjective and Bijective "Injective, Surjective and Bijective" tell you about how a function behaves. A function is a way of matching the members of a set "A" to a set "B":function

4. Slide 1- 4

5. Slide 1- 5

6. Slide 1- 6  Since each output of a one-to-one function comes from just one input, a one-to-one function can be reversed to send outputs back to the inputs from which they came.  The function defined by reversing a one-to-one function f is the inverse of f.  Composing a function with its inverse in either order sends each output back to the input from which it came.

7.  To find inverse: 1. Use the horizontal line test to determine if there is an inverse. 2. In the equation for f(x), replace f(x) with y 3. Interchange the roles of x and y, solve for y 4. Replace y by f -1 in the new equation 5. Verify!