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 f(x). This means you take the output of g(x) and use it as the input for f(x).

Front

Given f(x) = 5x + 7 and g(x) = 3 + 4x, find (f ∘ f)(x).

Back

(f ∘ f)(x) = f(f(x)) = f(5x + 7) = 5(5x + 7) + 7 = 25x + 35 + 7 = 25x + 42.

Front

What is the formula for (f ∘ f)(1) if f(x) = 5x + 7?

Back

(f ∘ f)(1) = f(f(1)) = f(5(1) + 7) = f(12) = 5(12) + 7 = 60 + 7 = 67.

Front

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

Back

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

Front

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

Back

g(5) = 5 - 2 = 3; then f(g(5)) = f(3) = 3(3) + 10 = 9 + 10 = 19.

Front

How do you evaluate f(-2) if f(x) = x + 3?

Back

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

Front

What is the significance of the notation (f ∘ g)(x)?

Back

It indicates that function g is applied first, followed by function f. It is essential for understanding the order of operations in composite functions.

Front

If f(x) = x + 3, what is f(0)?

Back

f(0) = 0 + 3 = 3.

Front

What is the result of (f ∘ g)(2) if f(x) = x^2 and g(x) = x + 1?

Back

(f ∘ g)(2) = f(g(2)) = f(2 + 1) = f(3) = 3^2 = 9.