1. Ch 1.6: Inverse of Functions and Relations

2. Inverse Functions
Two functions are inverses of each other if their compositions in both directions equals “x”
Ex: Verify if f(x) = 3x – 4 is an inverse of
YES!

3. Verify inverses by graphing: The inverse of a function will reflect its graph along y = x
One to One: each element in the domain does not share elements in the range 6 7 8 5 6 7 8 5
YES!
NO!

4. One to One continued… Algebraic Ex: f(x) = x2 f(1) = 12 f(-1) = (-1)2
NO!!
Graph: Horizontal line test
NO!
YES!

5. Find the Inverse of a function
Change the term f(x) to y (they mean the same)
Flip the spots of “x” and “y”
Solve this new equation for “y”
Change “y” to f-1(x)
Ex: Find the inverse of f(x) = 3x + 6