Ch 1.6: Inverse of Functions and Relations

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Ch 1.6: Inverse of Functions and Relations

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!

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!

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

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