🧠 Composition of Functions: Show Your Thinking (F-BF.A.1c)

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Compose functions. Solve each problem and show your work.

1. f(x) = 4x + 3, g(x) = 4x². Find (f ∘ g)(-4).

Show your work

2. f(x) = 6x + 6, g(x) = x². Find (g ∘ f)(1).

Show your work

3. f(x) = 6x − 4, g(x) = 4x². Find (f ∘ g)(1).

Show your work

4. f(x) = 4x − 3, g(x) = 4x². Find (g ∘ f)(1).

Show your work

5. f(x) = 4x − 3, g(x) = 4x². Find (f ∘ g)(4).

Show your work

6. f(x) = 4x + 6, g(x) = x². Find (g ∘ f)(-1).

Show your work

Explain: How did you solve problem 1? Could you check it another way?

Answer key: 1) 259 · 2) 144 · 3) 20 · 4) 4 · 5) 253 · 6) 4

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Worksheets › Grade 12 Math (Precalculus & Statistics) › Composition of Functions › Composition of Functions

Grade 12 (ages 17–18)Numbers & mathsFree printable PDF

About this grade 12 worksheet

Free Grade 12 Precalculus & Statistics math worksheet (Common Core F-BF.A.1c): composition of functions — problems with space to show work and explain reasoning, with answer key. Skill: Compose functions. Level: Grade 12 — also suits Year 13 (UK).

For teachers: skills & standards

CCSS F-BF.A.1c: Compose functions
Works as a morning-work page, a centre/station activity, homework or an early-finisher task.

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What age is it for?

It is designed for Grade 12 (ages 17–18), but use it with any child who is ready.

What skills does it build?

Compose functions.

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More “Composition of Functions” printables (f-bf.a.1c: compose functions)

Composition of Functions: Practice A (F-BF.A.1c) · Composition of Functions: Practice B (F-BF.A.1c) · Composition of Functions: Mixed Practice & Reasoning (F-BF.A.1c) · Composition of Functions: Quick Check (F-BF.A.1c)

All 5 composition of functions sheets → · Grade 12 Math (Precalculus & Statistics): all 10 skills → · All Common Core grades

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