Finding the Inverse of a Function Algebraically Module 1 Day 6 Finding the Inverse of a Function Algebraically

Finding the Inverse of a Function Finding an inverse from ordered pairs 1. Switch the x and y. 2. Determine if the relation is still a function by seeing if any of the domains (x-values) are the same. Finding an inverse from a function 1. The f(x) can be changed to a y, since they are equivalent. 2. Switch the x and y. 3. Solve for y.

Examples: Find the inverses 1. f(x) = 4x – 9 2. f(x) = 3𝑥 2 +7 3. f(x) = 2+ 3 𝑥−7

Determining if two functions are inverses? Are two functions inverses? 1. Complete the composites of the functions. F[g(x)] and G[f(x)]. 2. Both answers should result in a solution of x for them to be inverses 3. If either of the composites doesn’t give a value of x,then the functions are not inverses

Examples: Prove whether or not the following functions are inverses f(x) = 3𝑥 2 +7 and g(x) = 𝑥−7 3 f(x) = 5x-9 and g(x) = 𝑥+9 5