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WAEC Further Mathematics 2011 Paper

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Question : 6

Total: 40

A function is defined by

f(x) = \frac{3x+1}{x^{2}-1}, x \neq \pm 1

. Find f(-3).

$-1\frac{1}{4}$
$-1$
$\frac{4}{5}$
$1$

Solution:

Concept:

Evaluating a rational function by direct substitution of the given input value.

Explanation:

The given function is

f(x) = \frac{3x+1}{x^{2}-1}

.

We need

f(-3)

, so substitute

x = -3

everywhere in the formula.

Numerator:

3(-3) + 1 = -9 + 1 = -8

.

Denominator:

(-3)^{2} - 1 = 9 - 1 = 8

.

Thus,

f(-3) = \frac{-8}{8} = -1

.

Since

x \neq \pm 1

, the substitution

x = -3

is allowed.

Answer:

f(-3) = -1

Correct option: B.

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