Chapter 5: Operations with Functions and Inverse Functions

These flashcards cover key concepts from Chapter 5 related to operations with functions, composition of functions, and inverse functions.

What is the result of adding the functions f(x) = 3x² + 7x and g(x) = 2x² - x - 1?

(f + g)(x) = 5x² + 6x - 1.

What is the expression for the combined income function I(x) from the cover charge and snack bar sales?

I(x) = -25x² + 500x + 7500.

Given the functions R(I) = 0.02I + 500 and I(n) = -0.0125n² + 25n, what does R represent?

R represents the monthly rent for a business space based on its income.

What is the profit function P(x) that shows the total profit the music venue will make?

P(x) = -25x² + 700x + 500.

How do you find the inverse of a function?

By exchanging the coordinates of each ordered pair; the domain of the relation becomes the range of its inverse.

What is the notation for the inverse of a function f(x)?

f^{-1}(x).

What do we conclude if fog = x and gof = x for two functions f and g?

That f and g are inverse functions.

If 20 students go on a school trip and the cost per person is given by C(x)/(N(x)), what represents C(x)?

C(x) = 72 + 15x.

In the context of the retail business example, how is income modeled based on the number of customers?

Income is modeled by the function I(n) = -0.0125n² + 25n.

What does N(t) represent in the lottery prediction example?

N(t) is a function to calculate the predicted annual lottery net income at any point t years in the future.