SPM 2023 Add Maths Paper 1, Question 6Functions

Solved on video in English and Bahasa Melayu · Form 4, Functions · 4:05 video

The question

(a)

Diagram 5 shows the graph of the function f(x) = |x − 3| + 1 for the domain −2 ≤ x ≤ 7. The value h is marked on the f(x)-axis at the height of one endpoint of the graph. Find the value of the other object of h.

(b)(i)

It is given that the functions f: x → 4x − 1 and g: x → 2x + 3. (b)(i) Find the value of p if f⁻¹(p) = 2.

(b)(ii)

Using the same functions f: x → 4x − 1 and g: x → 2x + 3, (b)(ii) find the value of x if fg(x) = 5f(2).

SPM 2023 Add Maths Paper 1, Question 6: the question as drawn in Eduly's video4:05

Part (a)

Step 1

From the graph, h is the image at the right endpoint x = 7: h = f(7) = |7 − 3| + 1 = 4 + 1 = 5.

Why this step

h is the height of the right endpoint, not 0. Read the endpoint's x = 7 off the graph and substitute it into f.

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

Final answer

x = −1 (h = 5)

Where students lose marks

Watch out: h = 5 is the image, not the answer. Solve f(x) = 5 to find the other object, x = −1.

Part (b)(i)

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

Final answer

p = 7

Where students lose marks

Watch out: the inverse idea is right, but check the arithmetic in (p + 1)/4 = 2. Multiply by 4 first, then subtract 1.

Part (b)(ii)

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

Final answer

x = 3

Where students lose marks

Watch out: fg(x) means apply g first, then f. Doing gf(x) gives 8x + 1 and the wrong answer x = 17/4.

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