Composite Functions Review

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 the other. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find f(g(x))?

Back

To find f(g(x)), you substitute g(x) into the function f. This means you take the output of g(x) and use it as the input for f.

Front

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

Back

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

Front

What is the process to find g(f(x))?

Back

To find g(f(x)), you first calculate f(x) and then substitute that result into g. This means you take the output of f(x) and use it as the input for g.

Front

Given f(x) = -3x + 7 and g(x) = 2x^2 - 8, find g(f(x)).

Back

g(f(x)) = g(-3x + 7) = 2(-3x + 7)^2 - 8 = 18x^2 - 84x + 90.

Front

What is the significance of the order of functions in composite functions?

Back

The order of functions in composite functions matters because (f ∘ g)(x) is not necessarily equal to (g ∘ f)(x). The output depends on which function is applied first.

Front

Given f(x) = 4x - 1 and g(x) = x^2 + 2x, find g(f(x)).

Back

g(f(x)) = g(4x - 1) = (4x - 1)^2 + 2(4x - 1) = 16x^2 - 16x + 1.

Front

What is the formula for finding the composite of two functions?

Back

The formula for finding the composite of two functions f and g is (f ∘ g)(x) = f(g(x)).

Front

If f(x) = 2x - 8 and g(x) = 4x, what is g(f(x))?

Back

g(f(x)) = g(2x - 8) = 4(2x - 8) = 8x - 32.

Front

What is the domain of a composite function?

Back

The domain of a composite function (f ∘ g)(x) is the set of all x in the domain of g such that g(x) is in the domain of f.