Selangor Trial 2025 Add Maths Paper 1, Question 13Functions

Solved on video in English · Form 4, Functions · 5:54 video

The question

(a)

(Section B) Diagram 7 shows a relation that maps set X to set Y. Determine whether the given relation is a function or not. Give your justification.

(b)

(b) It is given that f : x → 4x + b, such that b is a constant. Express x in terms of b, if f²(x) = f(x).

(c)(i)

(c) Function g is defined by g : x → x/3. (i) State the function g⁻¹(x).

(c)(ii)

(c)(ii) Show that (g²)⁻¹(x) = (g⁻¹)²(x), where g : x → x/3.

Selangor Trial 2025 Add Maths Paper 1, Question 13: the question as drawn in Eduly's video5:54

Part (a)

Step 1

For a relation to be a function, every object in the domain X must map to exactly one image in Y.

Why this step

Check every object in X, one by one. Two objects may share an image, but each object needs exactly one image, not none and not two.

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

Final answer

Not a function, because object B has no image.

Where students lose marks

Watch out: check every object in X. B has no image, and you must state this reason, not just 'not a function'.

Part (b)

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

Final answer

x = −b/3

Where students lose marks

Watch out: f²(x) means f(f(x)), not (4x + b)². Also add the outer + b when composing, giving 16x + 5b.

Part (c)(i)

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

Final answer

g⁻¹(x) = 3x

Where students lose marks

Watch out: the inverse is not the reciprocal (not 3/x). After making x the subject, swap y back to x.

Part (c)(ii)

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

Final answer

Shown: (g²)⁻¹(x) = 9x = (g⁻¹)²(x)

Where students lose marks

Watch out: g²(x) means g(g(x)) = x/9, not [g(x)]² = x²/9. Work out both sides separately before comparing.

Watch every step of this question solved on video (5:54), with the reason behind each step and a box that checks your own answer.

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