1 5 Inverse Functions Properties Domain and Range

1. 5 Inverse Functions Properties, Domain and Range

Goal You should be able to determine the inverse of linear functions and state their properties.

Inverse Functions The reverse of the original function Maps each output value back to the corresponding input value The "undo" of a function

Inverse Functions The inverse of a linear function is the reverse of the original function. It can be found by performing the inverse operations (division instead of multiplication, say) in reverse order. f(x) = 2 x – 3 f-1(x) = x + 3 2

Inverse Functions It can be found by exchanging the x and y variables in the expression and solving for y: y = 5 x + 8 (exchange x and y) x = 5 y + 8 y = x – 8 5

Inverse Functions The inverse of a function is not necessarily a function itself. The inverse function of f(x) is written as f 1(x). If (a, b) is a point on the function y = f(x) then (b, a) is a point on y = f-1(x). Note: f-1(x) ≠ 1/f(x)

TOV f(x) f-1(x)

Mapping Diagrams

Graphing Inverse Functions When graphing an inverse of a function, you reflect it across the y = x line (as (x, y) of the function is (y, x) of the inverse). Any points shared by both functions lie on y = x and are called invariant points (shared by both graphs) Complete 1. 5 notes worksheet

Domain and Range

Class/Home work Pg 46 #1 a, 2 – 4, 6, 7, 10, 12, 16, 17