Inverse Functions

Part 5: Summary

1. Complete each of the following formulas:

   Note that the last two of these are indefinite integrals, not definite integrals. All four of these are basic facts that you should know without having to look them up.

2. Given a function definition, y = f(x), describe in words how you would find the derivative of the inverse function f^-1. Carry out this process for y = e^x. The result should be a formula (one you know already) for the derivative of the natural logarithm function.

3. Suppose you know a formula for the derivative g'(x) of an unknown function g, and you also know that g(0) = 0. Explain how to write a formula for g(x) using definite integrals. Illustrate this process by finding a formula for the function g(x) = ln(x + 1), starting from the fact that g'(x) = 1/(x + 1).