6.3 Review and 6.4 Intro.

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Presentation transcript:

6.3 Review and 6.4 Intro

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))?

2. Applications 6.3 a) The cost (in dollars) of producing n sneakers in a factory is given by C(n) = 60n + 750. 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.

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.

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 0 2 4 6 y 3 0 -3 -6 Thus the domains and ranges are switched also x 3 0 -3 -6 y 0 2 4 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?

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