A signal processing system has a gain factor GGG defined by the function G(v)=v+8v−1G(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.
Determine the domain of GGG. Give your answer using set notation.
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.
By considering any turning points of GGG, determine whether GGG has an inverse function. Fully justify your answer.
Practise Edexcel A Level Maths 2.2 Functions and Mappings with exam-style questions for A Level Maths. 6 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.