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: Option C
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}})