WAEC 2023 · Paper 1 · Q9

If $f: x \rightarrow 2\tan x$ and $g: x \rightarrow \sqrt{x^2 + 8}$ , find $(g \circ f)(45^\circ)$ .

Worked solution (try it first)

$g \circ f$ means apply $f$ first: $f(45^\circ) = 2\tan 45^\circ$ , and $\tan 45^\circ = 1$ , so $f(45^\circ) = 2$ .
Now apply $g$ to 2: $g(2) = \sqrt{2^2 + 8} = \sqrt{12}$ .
Simplify: $\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$ , option D.