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)), you 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(5)).

Back

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

Front

What is the value of h(a) = 3 - 2a when a = -3?

Back

h(-3) = 3 - 2(-3) = 3 + 6 = 9.

Front

Given f(x) = x^2 + x and g(x) = 3x + 1, find f(g(4)).

Back

g(4) = 3(4) + 1 = 13; f(13) = 13^2 + 13 = 169 + 13 = 182.

Front

If f(x) = 2x and g(x) = x^2 + 3, what is 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(3)) if f(x) = 1/x and g(x) = x^2?

Back

f(g(3)) = f(3^2) = f(9) = 1/9.

Front

What is the domain of a composite function?

Back

The domain of a composite function f(g(x)) is the set of all x in the domain of g such that g(x) is in the domain of f.

Front

How do you evaluate a composite function step by step?

Back

1. Start with the innermost function. 2. Calculate its output. 3. Use that output as the input for the next function.

Front

What is the range of a composite function?

Back

The range of a composite function f(g(x)) is determined by the range of f applied to the range of g.