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WAEC Further Mathematics 2013 Paper

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Question : 5

Total: 40

If

f(x) = x^{2}

g(x) = \sin x

, find g o f.

$\sin^{2} x$
$\sin x^{2}$
$(\sin x)x^{2}$
$x \sin x$

Solution:

Concept:

Composition

g \circ f

means apply

f

first, then apply

g

to the result.

Explanation:

Given

f(x) = x^2

and

g(x) = \sin x

.

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

.

Since

f(x) = x^2

, substitute into

g

:

g(f(x)) = g(x^2)

.

Now evaluate

g

at

x^2

:

g(x^2) = \sin(x^2)

.

Thus,

g \circ f = \sin x^2

.

Option A,

\sin^2 x

, would be

f \circ g

, not

g \circ f

.

Answer:

B.

\sin x^2

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