SPM 2020 Add Maths Paper 1, Question 2Functions

Solved on video in English and Bahasa Melayu · 4 marks · Form 4, Functions · 3:23 video

The question

(a)

Diagram 2 shows the mapping of function f and function g⁻¹. The mapping is p --(f)--> q --(g⁻¹)--> r. Write a relation using function notation such that q is an object.

[2 marks]

(b)

Diagram 2 shows the mapping of function f and function g⁻¹, with p --(f)--> q --(g⁻¹)--> r. State the image of f⁻¹g(r).

[2 marks]

SPM 2020 Add Maths Paper 1, Question 2: the question as drawn in Eduly's video

3:23

Part (a)

Step 1

In the diagram the arrow g⁻¹ starts at q and ends at r, so q is the object and r is its image under g⁻¹.

Why this step

The object is the input, where an arrow starts. So pick the arrow leaving q. f(p) = q is a trap: there q is the image.

1 more step, with the reason for it, in the full solution

Final answer

g⁻¹(q) = r (or g⁻¹: q → r)

Where students lose marks

Watch out: use the arrow that starts at q, which is g⁻¹. Writing f(p) = q makes q the image, not the object.

Part (b)

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

Final answer

Where students lose marks

Watch out: g(r) = q is only the inside. Apply f⁻¹ to q to reach p; do not stop at q.

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SPM 2020 Add Maths Paper 1, Question 2Functions

The question

Part (a)

Part (b)

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