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If $f (x) = \log x, g (x) = x^{3}$ , then $f (g (a)) + f (g (b)) =$

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$f (g (a)) + f (g (a b))$

$g (f (a b))$

$f (g (a b))$

$g (f (a) + f (b))$

answer is B.

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Detailed Solution

$f (x) = \log x, g (x) = x^{3}$

$f (g (a)) + f (g (b)) = f (a^{3}) + f (b^{3})$

$= \log a^{3} + \log b^{3}$

$= 3 (\log a + \log b)$ $= 3 \log a b$

$= \log {(a b)}^{3}$ $= f (g (a b))$

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