SPM 2019 Add Maths Paper 1, Question 8Functions

Solved on video in English and Bahasa Melayu · 4 marks · Form 4, Functions · 4:35 video

The question

Diagram 2 shows the relation of three sets: Set X = {3}, Set Y = {a}, Set Z = {2}, with an arrow f from 3 (in X) to a (in Y), and an arrow g⁻¹ from a (in Y) to 2 (in Z). It is given that f: x -> 2x+3 and g⁻¹ f: x -> 3/x + 1, x ≠ 0. (a) If a student writes a = 10, determine whether the value is correct or wrong. Give your reason. (b) Find g⁻¹(x).

[4 marks]

SPM 2019 Add Maths Paper 1, Question 8: the question as drawn in Eduly's video4:35

Step 1

The arrow f maps 3 (in X) to a (in Y), so a = f(3).

Why this step

The arrow f starts at 3 and lands on a, so a is simply the output of f when the input is 3.

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

Final answer

(a) Wrong, a = f(3) = 9. (b) g⁻¹(x) = (x + 3)/(x − 3)

Where students lose marks

Watch out: g⁻¹f means f first, then g⁻¹. Substitute f⁻¹(x) into g⁻¹f(x) to isolate g⁻¹(x), and do not swap the order.

Watch every step of this question solved on video (4:35), with the reason behind each step and a box that checks your own answer.

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