Melaka Trial 2025 Add Maths Paper 1, Question 1Functions

Solved on video in English · Form 4, Functions · 3:53 video

The question

(a)

Diagram 1 shows two functions, h and g, that map set Q to set P and set Q to set R respectively. Given that h(x) = (2x + 1)/4 and g(x) = 2x − 3.

(a) Find the function that maps set P to set Q.

(b)

(b) Find the composite function that maps set P to set R.

Step 1

Function h maps set Q to set P, so the function that maps set P back to set Q is the inverse h⁻¹.

Why this step

h takes Q to P, so to go the other way we undo h. That is what an inverse does. No need to involve g here.

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

Final answer

h⁻¹(x) = (4x − 1)/2

Where students lose marks

Watch out: P → Q is the inverse of h, so find h⁻¹ without using g. Take care making x the subject.

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

Final answer

gh⁻¹(x) = 4x − 4

Where students lose marks

Watch out: use gh⁻¹ (h⁻¹ first, then g), not hg or gh, and check the sign at the end.

Watch every step of this question solved on video (3:53), with the reason behind each step and a box that checks your own answer.

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