VM266 7337
Calculus 2 Chapter 7.1
Inverse Functions Pairs
g=f^-1
conditions
f(g(x)) = y for evey y in R
f(f^-1(x)) = X FOR EVERY X IN DOMAIN OF F^-1
g(f(x)) = x for every x in D
f^-1(f(x)) = X FOR EVERY X IN DOMAIN OF F
One to One
Horizontal Line Test
One input - One output
unique fn
Increasing or Decreasing
f: D -> R is incresing for every D
determine the slope of the funtion
Converse
P <=> Q
Theorem 7.3
f: D -> R
g: R -> D
Theorem 7.7
derivative of inverse function
if a diffrentiable function f has an inverse function and if f'(g(c)) does not equal 0 then g is differentiable at c
the derivative of the inverse function g is the reciprocal of the derivative f
Theorem 7.6
if f is continuous and increasing on [a.b] the f have an inverse function