If h(x) = x³ - {1}{x³}, evaluate h(a) - h≤ft(1/a).

Correct Answer is : 2a3−2a32a³ - {2}{a³}2a3−a32

Correct Answer is : 2a3−2a32a³ - {2}{a³}2a3−a32

Test Index

WAEC Further Mathematics 2010 Paper

Question : 34

Total: 40

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

h(a) - h\left(\frac{1}{a}\right)

Solution:

Concept:

Evaluate the function at two inputs and subtract the results.

Explanation:

Given

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

, substitute

x = a

h(a) = a^{3} - \frac{1}{a^{3}}

Now substitute

x = \frac{1}{a}

h\left(\frac{1}{a}\right) = \left(\frac{1}{a}\right)^{3} - \frac{1}{\left(\frac{1}{a}\right)^{3}} = \frac{1}{a^{3}} - a^{3}

Subtract the two results.

h(a) - h\left(\frac{1}{a}\right) = \left(a^{3} - \frac{1}{a^{3}}\right) - \left(\frac{1}{a^{3}} - a^{3}\right)

Simplify by distributing the negative sign.

= a^{3} - \frac{1}{a^{3}} - \frac{1}{a^{3}} + a^{3}

= 2a^{3} - \frac{2}{a^{3}}

Answer:

2a^{3} - \frac{2}{a^{3}}

, which is option C.

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