SPM 2023 Add Maths Paper 1, Question 14Functions

Solved on video in English and Bahasa Melayu · Form 4, Functions · 6:20 video

The question

(a)

It is given that f(x) = 2x − 5 and gf(x) = 4/(2x − 5), x ≠ h. (a) State the value of h.

(b)

Using f(x) = 2x − 5, (b) find the value of x when f(x) maps onto itself.

(c)(i)

Using f(x) = 2x − 5 and gf(x) = 4/(2x − 5), find (c)(i) g(x).

(c)(ii)

Using g(x) = 4/x from part (c)(i), find (c)(ii) g⁴n−3)(x), where n = 1, 2, 3, ...

SPM 2023 Add Maths Paper 1, Question 14: the question as drawn in Eduly's video6:20

Part (a)

Step 1

gf(x) = 4/(2x − 5) is undefined when its denominator is zero.

Why this step

You can't divide by zero, so we look for the x that makes the denominator 0. That is the value x must exclude.

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

Final answer

h = 5/2

Where students lose marks

Watch out: after solving 2x − 5 = 0, state the final value carefully as h = 5/2, not a mis-copied version.

Part (b)

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

Final answer

x = 5

Where students lose marks

Watch out: 'maps onto itself' means image = object, so set f(x) = x. Do not set f(x) = 0 or f²(x) = 0.

Part (c)(i)

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

Final answer

g(x) = 4/x, x ≠ 0

Where students lose marks

Watch out: state the condition x ≠ 0 together with g(x) = 4/x, because the function is undefined at x = 0.

Part (c)(ii)

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

Final answer

g⁴n−3)(x) = 4/x, x ≠ 0

Where students lose marks

Watch out: 4n − 3 is odd, not even. Odd compositions of g give 4/x, so do not conclude g⁴n−3)(x) = x.

Watch every step of this question solved on video (6:20), with the reason behind each step and a box that checks your own answer.

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