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WAEC Further Mathematics 2013 Paper

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Question : 35

Total: 40

If

g(x) = \frac{x+1}{x-2}, x \neq -2

g^{-1}(2)

.

3
2
$\frac{3}{4}$
-3

Solution:

Concept:

g^{-1}(2)

is the value of

x

for which

g(x)=2

.

Explanation:

Let

g(x)=\frac{x+1}{x+2}

, where

x\neq -2

.

Start with

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

.

Interchange

x

and

y

to get the inverse:

x=\frac{y+1}{y+2}.

Multiply through by

y+2

:

x(y+2)=y+1.

Expand:

xy+2x=y+1.

Collect

y

-terms on one side:

xy-y=1-2x.

Factor out

y

:

y(x-1)=1-2x.

Therefore,

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

Evaluate at

x=2

:

g^{-1}(2)=\frac{1-2(2)}{2-1}=\frac{1-4}{1}=-3.

Answer:

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

, so the correct option is D.

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