10 The function h is defined by
$$\mathrm { h } ( x ) = \frac { \sqrt { x } } { x - 3 }$$
where \(h\) has its maximum possible domain.
10
- Find the domain of h .
Give your answer using set notation.
10 - Alice correctly calculates
$$h ( 1 ) = - 0.5 \text { and } h ( 4 ) = 2$$
She then argues that since there is a change of sign there must be a value of \(x\) in the interval \(1 < x < 4\) that gives \(\mathrm { h } ( x ) = 0\)
Explain the error in Alice's argument.
[0pt]
[2 marks]
10 - By considering any turning points of h , determine whether h has an inverse function.
Fully justify your answer.
[0pt]
[6 marks]