Exercises: (+) Compose Functions

Work through each section in order. For composition, always identify the inner function first, then apply the outer function to the result.

Grade 9·21 problems·~28 min·Common Core Math - HS Functions·standard·hsf-bf-a-1c

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Warm-Up: Review What You Know

In the composition $f(g(x))$ , which function is applied first?

$f$ — it appears first reading left to right

$g$ — the inner function is evaluated first

Both are applied simultaneously

$f$ — it is on the outside, so it takes priority

Which of the following best describes what $f(g(x))$ means?

Multiply $f(x)$ and $g(x)$

Add $f(x)$ and $g(x)$

Use $g(x)$ as the input to $f$

Use $f(x)$ as the input to $g$

Using the values $f(3) = 7$ and $g(2) = 3$ , what is $f(g(2))$ ?

Let $f(x) = 2x + 1$ and $g(x) = x^2$ . Evaluate $f(g(3))$ .

Let $f(x) = 2x + 1$ and $g(x) = x^2$ . Evaluate $g(f(3))$ .

Let $f(x) = \sqrt{x}$ and $g(x) = x + 9$ . Find $f(g(x))$ and evaluate at $x = 7$ .

Let $f(x) = x^2$ and $g(x) = 3x - 1$ . Simplify $f(g(x))$ . What is the coefficient of $x^2$ in the simplified expression?

Let $f(x) = x + 5$ and $g(x) = 2x$ . Simplify $g(f(x))$ . What is the coefficient of $x$ in the simplified expression?

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