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WAEC Further Mathematics 2016 Paper

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Question : 5

Total: 40

If

f(x) = \; \frac{4}{x} - 1, x \neq 0

f^{-1}(7)

.

$\; \frac{-3}{7}$
$0$
$\; \frac{1}{2}$
$4$

Solution:

Concept:

To find

f^{-1}(7)

, first express

x

in terms of

y

from

y = f(x)

, then substitute

y = 7

.

Explanation:

Let

y = f(x)

.

y = \frac{4}{x} - 1

Since

x \neq 0

, combine terms:

y = \frac{4 - x}{x}

Multiply both sides by

x

:

xy = 4 - x

Bring

x

-terms together:

xy + x = 4

Factor out

x

:

x(y + 1) = 4

Hence,

x = \frac{4}{y + 1}

Therefore,

f^{-1}(y) = \frac{4}{y + 1}

Now substitute

y = 7

:

f^{-1}(7) = \frac{4}{7 + 1} = \frac{4}{8} = \frac{1}{2}

Answer:

\frac{1}{2}

Option C.

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