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 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)), substitute g(x) into the function f. This means you replace every instance of x in f with g(x).

Front

Given f(x) = 2x and g(x) = x² + 3, find f(g(x)).

Back

f(g(x)) = f(x² + 3) = 2(x² + 3) = 2x² + 6.

Front

What is the difference of two functions, (f - g)(x)?

Back

The difference of two functions is found by subtracting the output of g from the output of f: (f - g)(x) = f(x) - g(x).

Front

Given f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f - g)(x).

Back

(f - g)(x) = (3x² + 7x) - (2x² - x - 1) = x² + 8x + 1.

Front

What is the notation for composite functions?

Back

Composite functions are denoted as (f ∘ g)(x) or f(g(x)).

Front

Given f(x) = -3x + 7 and g(x) = 2x² - 8, find f(g(x)).

Back

f(g(x)) = f(2x² - 8) = -3(2x² - 8) + 7 = -6x² + 31.

Front

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

Back

To find g(f(x)), substitute f(x) into the function g. Replace every instance of x in g with f(x).

Front

Given f(x) = -3x + 7 and g(x) = 2x² - 8, find g(f(x)).

Back

g(f(x)) = g(-3x + 7) = 2(-3x + 7)² - (-3x + 7) - 8 = 18x² - 84x + 90.

Front

What is the output of g(f(-10)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

g(f(-10)) = g(3(-10) + 10) = g(-20) = -20 - 2 = -22.