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 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 value of f(-1) if f(x) = 2x² + 5x - 17?

Back

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

Front

Given f(x) = 2x + 25, find f(5).

Back

f(5) = 2(5) + 25 = 10 + 25 = 35.

Front

If 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 formula for finding the composite function (f ∘ g)(x)?

Back

(f ∘ g)(x) = f(g(x)).

Front

If f(x) = x² and g(x) = 3x - 1, find f(g(x)).

Back

f(g(x)) = f(3x - 1) = (3x - 1)² = 9x² - 6x + 1.

Front

What is the output of f(g(5)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

The output is 19.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the variable into the function's equation.