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)).

Tags

CCSS.HSF-BF.A.1C

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).

Tags

CCSS.HSF-BF.A.1C

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.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

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

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF-BF.A.1C

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.

Tags

CCSS.HSF-BF.A.1C

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.

Tags

CCSS.HSF-BF.A.1C

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.

Tags

CCSS.HSF-BF.A.1C

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.

Tags

CCSS.HSF-BF.A.1C

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.

Tags

CCSS.HSF-BF.A.1C