Let $f(x) = \frac{{4 - {x^2}}}{{4 - \sqrt x }}$.

(a)     State the largest possible domain for f.

(b)     Solve the inequality $f(x) \geqslant 1$.

(a)     $x \geqslant 0$ and $x \ne 16$     A1A1

(b)

     graph not to scale

finding crossing points     (M1)

e.g. $4 - {x^2} = 4 - \sqrt x$

x = 0 or x = 1     (A1)

$0 \leqslant x \leqslant 1$ or $x > 16$     A1A1

Note: Award M1A1A1A0 for solving the inequality only for the case $x < 16$.

[6 marks]

Most students were able to obtain partial marks, but there were very few completely correct answers.