Composite Functions

Front

What is a composite function?

Back

A composite function is a function that is formed by combining two functions, where the output of one function becomes the input of another. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

If f(x) = x^2 and g(x) = √x, what is g(f(x))?

Back

g(f(x)) = g(x^2) = √(x^2) = |x|.

Front

How do you find the value of f(g(3)) if f(x) = 2x + 1 and g(x) = x^2?

Back

First, find g(3): g(3) = 3^2 = 9. Then, find f(9): f(9) = 2(9) + 1 = 19.

Front

What is the formula for adding two functions f(x) and g(x)?

Back

The formula for adding two functions is (f + g)(x) = f(x) + g(x).

Front

If f(x) = x^2 + 3 and g(x) = 2x, what is (f + g)(x)?

Back

(f + g)(x) = (x^2 + 3) + (2x) = x^2 + 2x + 3.

Front

What is the output of f(-1) if f(x) = 2x^2 + 5x - 17?

Back

f(-1) = 2(-1)^2 + 5(-1) - 17 = 2 - 5 - 17 = -20.

Front

What is the definition of the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

If f(x) = -3x + 7, what is f(2)?

Back

f(2) = -3(2) + 7 = -6 + 7 = 1.

Front

What is the composition of functions f(x) = x + 1 and g(x) = 2x?

Back

(f ∘ g)(x) = f(g(x)) = f(2x) = 2x + 1.

Front

If g(x) = 2x^2 - 8, what is g(f(x)) if f(x) = -3x + 7?

Back

g(f(x)) = g(-3x + 7) = 2(-3x + 7)^2 - 8.