BitWithBite
Mathematics Worksheet
🎛️ Functions
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After this worksheet you can
Compute the composition of functions.Recognise an injective (one-to-one) function.Recognise a surjective (onto) function.Recognise a bijective function.📚 Quick Recap
A function is a special type of relation where every input maps to exactly one output — one of the most fundamental building blocks across all of mathematics.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1Let f(x)=x−2, g(x)=3x. (f ∘ g)(4) = ?
2Let f(x)=x−2, g(x)=3x. (g ∘ f)(4) = ?
3Is f(x) = 5x − 1 injective?
4Is f(x) = x2 + 1 injective on all real numbers?
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5(f ∘ g)(x) applies first.
6A one-to-one function is .
7Let f(x)=x−2 and g(x)=3x. Find (f ∘ g)(4).
8Let f(x)=x−2 and g(x)=3x. Find (g ∘ f)(4).
9Is f(x) = 5x − 1 injective?
🚀 Section C · Challenge ● CHALLENGE 5
10Is f(x) = x2 + 1 injective on all real numbers?
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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1-A 2-A 3-A 4-B | 5 g 6 injective 7 = f(g(4)) = f(12) = 10 8 = g(f(4)) = g(2) = 6 9 = Yes | 10 = No, f(1) = f(−1) = 2