Melaka Trial 2025 Add Maths Paper 2, Question 5Functions

Solved on video in English · Form 4, Functions · 5:01 video

The question

(a)

Given that f : x → m/x + n, x ≠ 0, and ff(x) = f⁻¹(x). Show that m + n² = 0.

(b)

Given that f(x) = 2x − 3, find the values of p if ff⁻¹(p − 2) = 3/p, p ≠ 0.

Step 1

Find the inverse: let y = m/x + n, then x = m/(y − n), so f⁻¹(x) = m/(x − n).

Why this step

We need f⁻¹ as a formula to compare with ff(x). Make x the subject of y = m/x + n first, then rename y as x.

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

Final answer

Shown: m + n² = 0

Where students lose marks

Watch out: invert f carefully (make x the subject first), and fully simplify ff(x) = f⁻¹(x) before comparing anything.

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

Final answer

p = −1 or p = 3

Where students lose marks

Watch out: ff⁻¹(x) = x, so skip finding f⁻¹. And when solving the quadratic, keep the negative root p = −1.

Watch every step of this question solved on video (5:01), with the reason behind each step and a box that checks your own answer.

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