If \(h(x) = x^{3} - \frac{1}{x^{3}}\), evaluate \(h(a) - h(\frac{1}{a})\).
FURTHER MATHEMATICS
WAEC 2010
If \(h(x) = x^{3} - \frac{1}{x^{3}}\), evaluate \(h(a) - h(\frac{1}{a})\).
- A. -1
- B. 0
- C. \(2a^{3} - \frac{2}{a^{3}}\)
- D. \(\frac{2}{a^{3}} - 2a^{3}\)
Correct Answer: C. \(2a^{3} - \frac{2}{a^{3}}\)
Explanation
\(h(x) = x^{3} - \frac{1}{x^{3}}\)
\(h(a) = a^{3} - \frac{1}{a^{3}}\)
\(h(\frac{1}{a}) = (\frac{1}{a})^{3} - \frac{1}{(\frac{1}{a})^{3}} = \frac{1}{a^{3}} - a^{3}\)
\(h(a) - h(\frac{1}{a}) = (a^{3} - \frac{1}{a^{3}}) - (\frac{1}{a^{3}} - a^{3}) = 2a^{3} - \frac{2}{a^{3}}\)
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