1. 6.3 Review and 6.4 Intro

2. 1. Review 6.3 Let f(x) = x2- 4 and g(x) = 3x + 1 Find f(8) ( , )
When does g(x) = -14? ( , )
What is (f+g)(1)?
What is the value of the f(g(-2))?

3. 2. Applications 6.3
a) The cost (in dollars) of producing n sneakers in a factory is given by C(n) = 60n The number of sneakers produced in t hours is given by N(t) = 50t. Write an expression for C(N(t)). Then find C(N(5)) and explain what it means.

4. b) You are going to buy a new sweatshirt
b) You are going to buy a new sweatshirt. There is a 25% discount right now, but you must pay 7% sales tax. Write a function showing the discount using the function D and p for the original price. Write an equation for the sales tax using the function T and p for the original price. Write a function for the actual cost of the sweatshirt using a composition of your two functions.

5. 3. Intro to 6.4
An inverse of a function is a function in which the x values of the original function become the y values and vice versa. x y Thus the domains and ranges are switched also x y

6. Finding an equation for an inverse function is easy
Finding an equation for an inverse function is easy. Just switch x and y. We then usually rewrite by solving for y.
Find the inverse of y = 2x – 1.
Graph both equations. What do you notice?

7. Find the inverses. b) f(x) = 1 2 x + 5 c) f(x) = 𝑥+3 7
d) f(x) = x3 + 8

8. Notice that inverses “undo” one another
Let’s say that you make $7 per hour plus 3% commission selling jewelry. Write an equation using x for the amount of jewelry sold and y for your hourly wage.
Find the inverse of this function. What do x and y represent in the inverse? How much jewelry did you sell if you made $10 in an hour?