MRSM Trial 2025 Add Maths Paper 1, Question 15Functions

Solved on video in English · Form 4, Functions · 5:20 video

The question

(a)

Diagram 5.1 shows the relation of three sets: Set A (element x) maps to Set B (element h(x)), which is then mapped by g to Set C (element 22k − 15x). It is given that g(x) = 2k + 5x. If h(m + k) = a, express m in terms of a and k.

(b)

Given g(x) = 2k + 5x, find g⁻¹(x) when k = −2 and hence verify that the g⁻¹(x) obtained is the inverse function of g(x).

(c)

Diagram 5.2 shows the graph of function g(x), drawn as a line segment from (1, 1) to (r, s). Sketch the graph of g⁻¹(x) on Diagram 5.2.

MRSM Trial 2025 Add Maths Paper 1, Question 15: the question as drawn in Eduly's video

5:20

Part (a)

Step 1

The composite from Set A to Set C is g(h(x)) = 22k − 15x.

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

Final answer

m = (k − a)/3

Where students lose marks

Watch out: extract h(x) first, expand −3(m + k) with care, and give m in terms of a and k, not x.

Part (b)

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

Final answer

g⁻¹(x) = (x + 4)/5; gg⁻¹(x) = g⁻¹g(x) = x

Where students lose marks

Watch out: substitute k = −2 before inverting, and check both gg⁻¹(x) and g⁻¹g(x), not just one.

Part (c)

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

Final answer

Sketch: reflect g in y = x, ends (1, 1) and (s, r)

Where students lose marks

Watch out: reflect in the line y = x (not an axis), swap (r, s) to (s, r), and show the mirror line.

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MRSM Trial 2025 Add Maths Paper 1, Question 15Functions

The question

Part (a)

Part (b)

Part (c)

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