Chapter 6: Inverse Functions

Chapter 6

6.1 Exponential Functions and Their Derivatives

- one-to-one tells if a function has an inverse or not
- if function does not pass the Horizontal Line test it isn't one-to-one
- two inputs cannot have the same output to be one-to-one
Inverse= outputs of f(x) are now inputs of the inverse of f(x), inputs of f(x) are now ouputs of the inverse of f(x)
- to find the inverse switch x and y and solve for y
Theorem 7
- if f is one-to-one at the inverse of f(a) then inverse of f(a)=1/f ' (inverse of f(a))

6.2 The Natural Exponential Function

ln(g(x))'=g'(x)/g(x)

ln(1)=0                     e^0=1

integral(1/x)= ln(x) + c

Logarithmic Differentiation= take natural log of both sides and the differentiate

EX. y=(x^2+2)^2