WAEC - Further Mathematics (2010 - No. 34)
If \(h(x) = x^{3} - \frac{1}{x^{3}}\), evaluate \(h(a) - h(\frac{1}{a})\).
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\(2a^{3} - \frac{2}{a^{3}}\)
\(\frac{2}{a^{3}} - 2a^{3}\)
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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