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WAEC Further Mathematics 2023 Paper

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Question : 21

Total: 40

If

f : x \rightarrow 2 \tan x

g : x \rightarrow \sqrt{x^2 + 8}, \text{ find } \text{(g o f)}(45^{\circ})

4
2√3
6
3√2

Solution:

Concept:

Composite functions require substituting one function into another before evaluating at the given input.

Explanation:

Given

f(x) = 2\tan x

and

g(x) = \sqrt{x^2 + 8}

.

The composite function is

(g \circ f)(x) = g(f(x))

.

Substitute

f(x)

into

g(x)

:

(g \circ f)(x) = \sqrt{(2\tan x)^2 + 8}

.

Now evaluate at

x = 45^{\circ}

:

\tan 45^{\circ} = 1

, so

2\tan 45^{\circ} = 2

.

Thus,

(g \circ f)(45^{\circ}) = \sqrt{2^2 + 8} = \sqrt{4 + 8}

.

Simplify:

\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}

.

Answer:

2\sqrt{3}

(Option B).

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