A Level Mathematics AQA – OCR Paper 2 – Pure Mathematics & Mechanics Set 1.

A Level Mathematics AQA
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– OCR
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Paper 2 – Pure Mathematics & Mechanics Set
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1

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,Sectioni Ai –i Purei Mathematics
Questioni 1

Thei functioni 𝑓i isi definedi by

𝑓(𝑥) = 3 + 3−𝑥
i i i i i ,i i 𝑥 ∈ ℝ
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(i) Usingi seti notation,i statei thei rangei ofi 𝑓




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(ii) Usingi seti notation,i statei thei domaini ofi 𝑓−1




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(iii) Findi ani expressioni fori 𝑓−1




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, Thei functioni 𝑔i isi definedi by

𝑔(𝑥) = 3 + √𝑥
i i i i i ,i i (𝑥 ∈ ℝ ∶ 𝑥 > 0)
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(iv) Findi ani expressioni fori 𝑔𝑓(𝑥)




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(v) Solvei thei equationi 𝑔𝑓(𝑥)i = 5,i i givingi youri answeri ini ani exacti form.




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(Totali 10i Marks)