The function fff is defined by
f(x)=xx−5 f(x) = \frac{\sqrt{x}}{x - 5} f(x)=x−5xwhere fff has its maximum possible domain.
Find the domain of fff. Give your answer using set notation.
Bob correctly calculates f(4)=−2f(4) = -2f(4)=−2 and f(9)=0.75f(9) = 0.75f(9)=0.75. He argues that because there is a change of sign, there must be a value of xxx in the interval 4<x<94 < x < 94<x<9 such that f(x)=0f(x) = 0f(x)=0. Explain the error in Bob's argument.
By considering any turning points of fff, determine whether fff has an inverse function. Fully justify your answer.
Practise AQA A Level Maths 1.1 OT1: Mathematical argument, language and proof with exam-style questions for A Level Maths. 8 questions 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, matched to the AQA A Level Maths (7357) 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.
