Selangor Trial 2025 Add Maths Paper 2, Question 3Functions

Solved on video in English · Form 4, Functions · 5:00 video

The question

(a)(i)

It is given that the function f : x → 2x and the function g : x → √(x − 4). (a)(i) Find the value of gf(10).

(a)(ii)

(a)(ii) Find the value of x when f²(x) = 1.

(b)

(b) Determine the function h(x) such that hg(x) = x + 3. Hence, find the value of h(−3).

Step 1

Work from the inside out: first find f(10) = 2(10) = 20.

Why this step

The function written closest to the input acts first, so gf(10) means f first, then g. Swapping the order gives fg(10), a different answer.

1 more step, with the reason for it, in the full solution

Final answer

gf(10) = 4

Where students lose marks

Watch out: gf means f first, then g. Also subtract 4 inside the square root before taking √.

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

Final answer

x = 1/4

Where students lose marks

Watch out: f²(x) means f(f(x)) = 4x, not [f(x)]² = 4x².

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

Final answer

h(x) = x² + 7, h(−3) = 16

Where students lose marks

Watch out: let u = √(x − 4) and write x in terms of u first. Also (−3)² = 9, not −9.

Watch every step of this question solved on video (5:00), with the reason behind each step and a box that checks your own answer.

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