O-LevelAdditional MathematicsFunctions4037/12 · Oct/Nov 2020 · Q65 Marks

f(x) = x²+2x-3 for x≥-1

(a)Given that the minimum value of x² + 2x-3 occurs when x =-1, explain why f(x) has an inverse.[1]
(b)On the axes below, sketch the graph of y = f(x) and the graph of y = f¯¹(x). Label each graph and state the intercepts on the coordinate axes.[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

B1 It is a one-one function because of the given restricted domain or because x ≥ −1
B1 for y = f(x) for x >−1 only
B1 for 1 on x-axis and –3 on y-axis for y = f(x)
B1 for y = f¯¹(x) as a reflection of y = f(x) in the line y = x, maybe implied by intercepts with axes
B1 for 1 on y-axis and -3 on x-axis for y = f¯¹(x)

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About this question

Topic

Functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.

Source

O-Level Additional Mathematics, Oct/Nov 2020 Paper 1 Variant 2, question 6.

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