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WAEC Further Mathematics 2025 Paper

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Question : 9

Total: 40

If f(x) =

\frac{1}{2 - x}

\neq

^{-1}

\frac{-1}{2}

)

-5
4
-7
-4

Solution:

Concept:

To find

f^{-1}\left(-\frac{1}{2}\right)

, first express

x

in terms of

y

from

y = f(x)

and then substitute the given value.

Explanation:

Let

y = f(x) = \frac{1}{2 - x}

.

Then

y = \frac{1}{2 - x}

.

Multiply both sides by

2 - x

:

y(2 - x) = 1

.

Expand:

2y - xy = 1

.

Rearrange to make

x

the subject:

xy = 2y - 1

.

Divide by

y

:

x = \frac{2y - 1}{y}

.

Therefore,

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

.

Now substitute

x = -\frac{1}{2}

:

f^{-1}\left(-\frac{1}{2}\right) = \frac{2\left(-\frac{1}{2}\right) - 1}{-\frac{1}{2}}

.

Simplify the numerator:

-1 - 1 = -2

.

So

f^{-1}\left(-\frac{1}{2}\right) = \frac{-2}{-\frac{1}{2}} = -2 \times \frac{-2}{1} = 4

.

Answer:

4

(Option B)

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