Kuala Lumpur Trial 2025 Add Maths Paper 2, Question 1Functions

Solved on video in English · Form 4, Functions · 5:13 video

The question

(a)

Diagram 1 shows the relation between Set A, Set B and Set C, where g maps Set A (element x) to Set B (element 2x + 3) and f maps Set B to Set C (element z).

(a) By using function notation f and g, write a composite function to show the relation between Set A and Set C in terms of z.

(b)

(b) Given that fg(x) = x² − 1, find f(x). Hence, find the value of f(−2).

Kuala Lumpur Trial 2025 Add Maths Paper 2, Question 1: the question as drawn in Eduly's video5:13

Part (a)

Step 1

g takes Set A to Set B and f takes Set B to Set C, so applying g first then f takes Set A straight to Set C.

2 more steps, each with the reason for it, in the full solution

Final answer

fg(x) = z

Where students lose marks

Watch out: write fg(x), not gf(x). The function next to x (g) acts first, and f is applied last.

Part (b)

5 more steps, each with the reason for it, in the full solution

Final answer

f(x) = (x² − 6x + 5)/4; f(−2) = 21/4

Where students lose marks

Watch out: read g(x) = 2x + 3 from the diagram to isolate f, and watch the sign: −6(−2) = +12, not −12.

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