Composite Functions - Edited

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 find (f∘g)(x)?

Back

To find (f∘g)(x), first evaluate g(x) and then substitute that result into f(x).

Front

Given f(x) = 3x + 10 and g(x) = x - 2, find (f∘g)(0).

Back

(f∘g)(0) = f(g(0)) = f(-2) = 4.

Front

What is the formula for (f∘f)(x)?

Back

(f∘f)(x) means applying function f to itself, calculated as f(f(x)).

Front

Given f(x) = 5x + 7, find (f∘f)(x) in simplest form.

Back

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

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

Given f(x) = √(4x - 4) and g(x) = 3x + 1, find (g∘f)(1).

Back

(g∘f)(1) = g(f(1)) = g(√(0)) = g(0) = 1.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Given f(x) = 2x² + 5x - 17, find f(-1).

Back

f(-1) = 2(-1)² + 5(-1) - 17 = -20.

Front

What is the notation for composite functions?

Back

Composite functions are denoted as (f∘g)(x), which means f(g(x)).