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3.1 Algebra and functions (A-level only)

3.1 Algebra and functions (A-level only)

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Question 19

A signal processing system has a gain factor GGG defined by the function

G(v)=v+8v−1 G(v) = \frac{\sqrt{v+8}}{v - 1} G(v)=v−1v+8​​

where GGG has its maximum possible domain in terms of the input voltage vvv.

a.

Determine the domain of GGG. Give your answer using set notation.

[2]
b.

An engineer calculates G(0)≈−2.83G(0) \approx -2.83G(0)≈−2.83 and G(2)≈3.16G(2) \approx 3.16G(2)≈3.16. They argue that because there is a change of sign, there must be a voltage vvv in the interval 0<v<20 < v < 20<v<2 such that the gain factor G(v)=0G(v) = 0G(v)=0. Explain the error in the engineer's argument.

[2]
c.

By considering any turning points of GGG, determine whether GGG has an inverse function. Fully justify your answer.

[4]
Markscheme

3.1 Algebra and functions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.1 Algebra and functions (A-level only)

281 exam-style questions on CCEA A Level Maths 3.1 Algebra and functions (A-level only), covering 3.1.1 Algebra and functions (A-level only), 3.1.2 Algebra and functions (A-level only), 3.1.3 Algebra and functions (A-level only), 3.1.4 Algebra and functions (A-level only), 3.1.5 Algebra and functions (A-level only), 3.1.6 Algebra and functions (A-level only), 3.1.7 Algebra and functions (A-level only), 3.1.8 Algebra and functions (A-level only), 3.1.9 Algebra and functions (A-level only), and 3.1 Algebra and functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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