SPM 2021 Add Maths Paper 2, Question 3Functions

Solved on video in English and Bahasa Melayu · Form 4, Functions · 4:21 video

The question

(a)

Diagram 1 shows the relation of three sets. Set P contains x, Set Q contains x + 2, and Set R contains 3x − 4. Function f maps Set P to Set Q and function g maps Set Q to Set R. Find (a) g(x).

(b)

Diagram 1 shows the relation of three sets, where function f maps x to x + 2. Find (b)(i) f²(x), (b)(ii) the function f^n(x), in terms of n and x.

SPM 2021 Add Maths Paper 2, Question 3: the question as drawn in Eduly's video4:21

Part (a)

Step 1

From the diagram, f maps x to x + 2, so f(x) = x + 2.

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

Final answer

g(x) = 3x − 10

Where students lose marks

Watch out: g(x) is not (3x − 4) − (x + 2). Find gf(x) first, then use f⁻¹ to get g.

Part (b)

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

Final answer

f²(x) = x + 4, f^n(x) = x + 2n

Where students lose marks

Watch out: don't stop at f²(x). Compute f³(x) too so you can spot the pattern for f^n(x).

Watch every step of this question solved on video (4:21), with the reason behind each step and a box that checks your own answer.

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