Pre-Calc Chapter 1 section 7 The Inverse of a Function

Inverse of a function A relation where the if the range value from the original function is put in as the domain value of the inverse, the domain of the first will be the ranger of the input Confused yet? f -1 (x)

Inverse function Un-does a function f(x) = x + 7f -1 (x) = x - 7 f(3) = 10f -1 (10) = 3

Inverse function f(x) 3 10 f -1 (x)

Inverse of a function must be a function

f(f -1 (a)) = a f -1 (f (a)) = a & For all values of a in the intersection of the range and the domain of f(x)

Find the inverse with algebra For a function f(x) Let y = f(x) Solve for x Re write with x = f -1 (x) and y = x

Find f(x) = 3x + 5 y = 3x + 5 y – 5 = 3x y – 5 = x 3 so f -1 (x) = y – 5 = x 3

Find f -1 (x) of f(x) = 3x 2 ; f(x) >= 0 y = 3x 2 y3 y3 = x 2 y3 y3 =x y3 y3 f -1 (x) = ; x >= 0

In a graph replace x with y So reflect the graph across the line x = y