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.