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WAEC Further Mathematics 2017 Paper

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Question : 38

Total: 40

Given that

f(x) = 2x^{2} - 3

g(x) = x + 1

x \in R

. Find g o f(x).

$2(x^{2} - 1)$
$2x^{2} + 4x - 1$
$2x^{2} + 6x - 1$
$3(x^{2} - 1)$

Solution:

Concept:

Composition of functions means applying

g(x)

to the output of

f(x)

.

Explanation:

Given

f(x) = 2x^{2} - 3

and

g(x) = x + 1

.

We need

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

.

Substitute

f(x)

into

g(x)

:

g(f(x)) = g(2x^{2} - 3)

.

Since

g(x) = x + 1

, replace

x

with

2x^{2} - 3

:

g(2x^{2} - 3) = (2x^{2} - 3) + 1

.

Simplify:

2x^{2} - 3 + 1 = 2x^{2} - 2

.

Factor out

2

:

2x^{2} - 2 = 2(x^{2} - 1)

.

Answer:

g \circ f(x) = 2(x^{2} - 1)

.

So the correct option is A.

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