5.5 Review

Front

What is the composition of functions?

Back

The composition of functions, denoted as (f ∘ g)(x), is the application of one function to the results of another. It is defined as (f ∘ g)(x) = f(g(x)).

Front

If f(x) = x^2 and g(x) = 3x - 1, what is g ∘ f(x)?

Back

g ∘ f(x) = g(f(x)) = g(x^2) = 3(x^2) - 1 = 3x^2 - 1.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function f(x) at a specific point a, substitute x with a in the function's expression, i.e., f(a).

Front

Given f(x) = x^2 + 5x - 17, find f(-1).

Back

f(-1) = (-1)^2 + 5(-1) - 17 = 1 - 5 - 17 = -21.

Front

What is the product of two functions f(x) and g(x)?

Back

The product of two functions, denoted as (f ⋅ g)(x), is defined as (f ⋅ g)(x) = f(x) * g(x).

Front

If f(x) = 2 and g(x) = -2x + 1, what is (f ⋅ g)(x)?

Back

(f ⋅ g)(x) = f(x) * g(x) = 2 * (-2x + 1) = -4x + 2.

Front

What does it mean for two functions to be equal?

Back

Two functions f(x) and g(x) are equal if for every x in their domain, f(x) = g(x).

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What is the difference between f(g(x)) and g(f(x))?

Back

f(g(x)) applies g first and then f to the result, while g(f(x)) applies f first and then g to the result. They are generally not equal.

Front

If f(x) = 3x + 10 and g(x) = x - 2, find f(g(5)).

Back

g(5) = 5 - 2 = 3; then f(g(5)) = f(3) = 3(3) + 10 = 19.