A function is defined by h : x → 2 - 1/2x-3, x ≠ 3/2. Find h^{-1}, the inverse of h.

Correct Answer is : 3x−72x−4,x≠23x-7/2x-4, x ≠ 22x−43x−7,x=2

Correct Answer is : 3x−72x−4,x≠23x-7/2x-4, x ≠ 22x−43x−7,x=2

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WAEC Further Mathematics 2014 Paper

Question : 15

Total: 40

h : x \to 2 - \frac{1}{2x-3}, x \neq \frac{3}{2}

h^{-1}

, the inverse of h.

Solution:

Concept:

To find the inverse of

h

, write

h(x)

as a single algebraic fraction, swap

x

and

y

, then solve for

y

Explanation:

Given

h(x)=2-\frac{1}{2x-3}

Combine into one fraction:

h(x)=\frac{2(2x-3)-1}{2x-3}=\frac{4x-7}{2x-3}

Let

y=\frac{4x-7}{2x-3}

Swap

x

and

y

for the inverse:

x=\frac{4y-7}{2y-3}

Cross multiply:

x(2y-3)=4y-7

Expand:

2xy-3x=4y-7

Collect terms containing

y

2xy-4y=3x-7

Factor out

y

y(2x-4)=3x-7

Therefore:

y=\frac{3x-7}{2x-4}

, with

x\neq2

Answer:

h^{-1}(x)=\frac{3x-7}{2x-4},\ x\neq2

This corresponds to Option B.

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