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.