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1.1 OT1: Mathematical argument, language and proof

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Question 2

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

1.1 OT1: Mathematical argument, language and proof Questions

  1. A Level
  2. /Maths
  3. /1.1 OT1: Mathematical argument, language and proof

7 exam-style questions on AQA A Level Maths 1.1 OT1: Mathematical argument, language and proof, covering 1.1.1 Constructing mathematical arguments, 1.1.2 Mathematical language and syntax, 1.1.3 Set theory language and symbols, 1.1.4 Definition, domain and range of functions, and 1.1.5 Comprehending and critiquing arguments. Each one has a worked solution and a mark scheme showing where the marks go.

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