Composite Functions

Front

What is a composite function?

Back

A composite function is a function that is formed by combining two functions, denoted as (f∘g)(x) = f(g(x)).

Front

How do you rewrite (f∘g)(x)?

Back

(f∘g)(x) can be rewritten as f(g(x)).

Front

Given f(x) = -3x + 7 and g(x) = 2x^2 - 8, what is f(g(-5))?

Back

f(g(-5)) = -119.

Front

What is the output of f(g(-1)) if f(x) = 2x and g(x) = x^2 + 3?

Back

f(g(-1)) = -3.

Front

How do you find f(g(x)) for f(x) = 2x and g(x) = x^2 + 3?

Back

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

Front

Back

The domain is x ≥ 1.

Front

What is the notation for composite functions?

Back

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

Front

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

Back

f(g(2)) = f(6) = 8.

Front

What is the range of a composite function?

Back

The range of a composite function depends on the range of the inner function and how it is transformed by the outer function.

Front

How do you evaluate a composite function step by step?

Back

1. Evaluate the inner function. 2. Substitute the result into the outer function.