1. 1.6 Inverse Functions

2. Review of things we already know One to One Function: That is, while a function specifies that every x has a unique y, a one to one function specifies that ALSO every y has a unique x. The horizontal line test

3. An Inverse Function is the inverse of if How to find an inverse? Switch x and y and solve for y. and

4. (2,1) (1,2) f(x) f -1 (x) Graph of an Inverse

5. Logarithms “logarithm” is the term for the inverse of any exponential function. y = 2 x  The inverse would be x = 2 y This is written officially as log 2 x = y

6. How to look at logarithms log b x = y can be thought of as log b n = p Then rewrite as n = b p (notice the significance of the variables chosen!!) And then solve it!

7. Some Rules 1.If log b x 1 = log b x 2 then x 1 = x 2 2.Log b b = 1 3.log b 1 = 0 4.log b b x = x 5.lne x = x 6.b log b x = x 7.e lnx = x 8.b x = e xlnb

8. There are 4 Laws of Simplification

9. Get out that graphing calculator!! Lets graph two functions and find their point of intersection. y = 3x and y = x 3