4-5

Inverses

Section 4-5 was about finding inverses. To find an inverse you have to use the horizontal line test. This is similar to the vertical line test. If it passes without touching two points then there is an inverse that is a function. That is the first step - drawing the graph.

After that, to find an inverse:

1. Switch x and y.

2. Solve for y.

To check if something is an inverse:

f(g(x)) = x and g(f(x)) = x

EXAMPLE 1: y = x + 4

A). First, graph the equation.

B). By using the horizontal line test, we know that there is an inverse.

C). Now, switch the x and y.

D). x = y + 4 and solve for y.

E). y^-1 = x - 4

* Place -1 above y to show that it is the inverse.

EXAMPLE 2: Prove that f(x) = x - 2 and f^-1(x) = x + 2 are inverses.

A). f(f^-1(x)) = (x + 2) - 2

= x

B). f^-1(f(x)) = ( x - 2) + 2

= x

C). This proves that these are inverses.