Pre-AP Pre-CalculusChapter 1, Section 5Parametric Relations and Inverses2013 - 2014

Inverse Relations & Inverse Functions

When you reverse the coordinates of all the ordered pair and solve for the dependent variable, you get an inverse relation.

If a function fails the horizontal line test, the inverse function will fail the vertical line test meaning the inverse relation is not a function.

Which of the 4 graphs are a function? Which ones have an inverse that is a function?

Definition: Inverse Function• If f is a one-to-one function with domain D and range R, then

the inverse function of f, denoted , is the function with domain R and range D defined by

if and only if

Find an equation for if

Show algebraically that and are inverse functions.

Show that has an inverse function and state any restrictions on the domains of f and .

Homework• Ch. 1.5: Pg. 135-136: 9 – 21 odd, 27, 31, 33, 41 – 44,