Warm Up #8 Sketch the graphs of: 1. 𝑓 𝑥 = 𝑥+2 2 −2 2. 𝑓 𝑥 = 𝑥−5 +3 1. 𝑓 𝑥 = 𝑥+2 2 −2 2. 𝑓 𝑥 = 𝑥−5 +3 𝑓 𝑥 = 𝑥 3 𝑔 𝑥 = 1 𝑥 3. Find 𝑓∘𝑔 4. Find 𝑔∘𝑓 5. Find 𝑓∘𝑓

Warm Up # 9 Find the domain: 1. 𝑓 𝑥 = 𝑥+1 2. 𝑓 𝑥 = 2 𝑥 2 −2𝑥 Simplify: 3. 7−10 7−𝑥 10 4. 3 2 𝑥 3 2 −2 +4 Solve for x in terms of y: 5. 𝑦= 3 2𝑥−4

1-6: Inverse Functions

Objectives You will be able to: Find the inverse of a function Graph the inverse of a function

Inverse Function An inverse function is when the domain and range switch, denoted by 𝑓 −1 𝑥 Ex. 𝑓 𝑥 = 1,5 , 2,6 , 3,7 , (4,8) 𝑓 −1 𝑥 = 5,1 , 6,2 , 7,3 , (8,4)

How to find the inverse of a function Replace 𝑓 x with y. Switch the x and the y. Solve for y. Replace y with 𝑓 −1 (x)

Example 1: Find the inverse of 𝑓 𝑥 =𝑥+2

Example 2: Find the inverse of 𝑓 𝑥 = 𝑥 3 −1

Not all functions have inverses A function has an inverse if it passes a horizontal line test Has an inverse Does not Have an inverse

Example 3: Does this function have an inverse?

Example 4: Sketch the graph of the inverse functions: 𝑓 𝑥 = 𝑥 2 , 𝑥≥0 𝑎𝑛𝑑 𝑓 −1 𝑥 = 𝑥

Example 5: Show that the functions are inverses (𝑓∘𝑔 𝑥 =𝑥 𝑎𝑛𝑑 𝑔∘𝑓 𝑥 =𝑥). 𝑓 𝑥 =2 𝑥 3 −1 𝑎𝑛𝑑 𝑔 𝑥 = 3 𝑥+1 2

Summary In this lesson we learned to: Find the inverse of a function Graph the inverse of a function

Warm Up # 12 1. Find the equation of the line that is horizontal, going through point (1,2) 2. Find f(6) when f(x) = 3x+5 3. Find the domain of 5 𝑥+1 4. X varies directly with the square of y and inversely with z. Write a general formula when x=16 y=4 and z=2