Functions & Graphs

CoreMaths revision

Functions

Treat functions as mappings with domains, compositions and inverses rather than just formulas.

Open calculator

Focus points

✓Use function notation.

✓Compose functions.

✓Find and verify inverse functions.

orin

Orin

The Wise Owl

Guides study flow, revision planning, and calmer focus sessions.

Practice set

Question lineup

Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.

8 revision questions

Question 1FluencyCore

Original practice · Free Online Revision

Skill · function evaluation

If f(x)=3x−5, find f(7).

Question 2FluencyCore

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Skill · function evaluation

If f(x)=x²+1, find f(−3).

Question 3FluencyCore

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Skill · composition

Given f(x)=2x+3 and g(x)=x², find (g∘f)(x).

Question 4FluencyCore

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Skill · composition

Given f(x)=2x+3 and g(x)=x², find (f∘g)(x).

Question 5FluencyCore

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Skill · inverse function

Find f⁻¹(x) for f(x)=5x−4.

Question 6FluencyCore

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Skill · domain

State the domain of h(x)=1/(x−6).

Question 7ReasoningCore

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Skill · inverse reasoning

Why does f(x)=x² on all real numbers not have an inverse function?

Question 8ChallengeStretch

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Skill · inverse rational function

If f(x)=(x−1)/(x+2), find f⁻¹(x).