Warmup Let f(x) = x – 3 and g(x) = x2. What is (f ○ g)(1)?

5-3 Inverse Functions and Relations Find the inverse of a function or a relation. Determine whether two functions or relations are inverses of each other.

Two functions f and g are inverses if the domain of f becomes the range of the g, and the range of f becomes the domain of g.

Find the inverse of each relation 2. {(-2, 9), (4, -1), (-7, 9), (7, 0)}

Method for finding inverses Replace f(x) with y. Interchange x and y. Solve for y if possible If there is only one y-value possible for each x-value in the inverse, you can write the inverse with function notation, and it is called f -1(x) (read this as f inverse of x)

Find the inverse of each function. Then graph the function. 4. 𝑔(𝑥)=4𝑥−6

Find the inverse of each function. Then graph the function.

A function and its inverse are reflections across the line y = x When you describe a function and then describe its inverse, you can see that the steps in the function are reversed, and you have inverse operations (they undo each other) #4 𝑔 𝑥 =4𝑥 −6 𝑔 −1 𝑥 = 𝑥+6 4

Find the inverse of each function Find the inverse of each function. Then graph the function and its inverse. 23. 𝑓 𝑥 = 𝑥+1 2 +3

Horizontal line test checks to see if a function has an inverse function Use the horizontal line test to determine whether the inverse of each function is also a function.