The function $g$ is defined for all nonzero $x$ by... | Free GMAT Practice Question | GMAT Panda

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The function g is defined for all nonzero x by the equation g (x) = x^{3} - \frac{1}{x ^{3}} . If x is not equal to 0, which of the following equals g (\frac{1}{x}) ?

Explanation	Calculations	Help
$We substitute \frac{1}{x} into the definition of g .$	$g (\frac{1}{x}) = (\frac{1}{x})^{3} - \frac{1}{( \frac{1}{x} ) ^{3}}$	Theory & Tactics Method Card ALG5-A Click to view full details
$We simplify each power and reciprocal.$	$g (\frac{1}{x}) = \frac{1}{x ^{3}} - x^{3}$
$We factor out a negative to match the original function form.$	$\frac{1}{x ^{3}} - x^{3} = - (x^{3} - \frac{1}{x ^{3}}) = - g (x)$
$We verify that g (- x) also equals this same expression.$	$g (- x) = (- x)^{3} - \frac{1}{( - x ) ^{3}} = - x^{3} + \frac{1}{x ^{3}} = - (x^{3} - \frac{1}{x ^{3}}) = - g (x)$

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B

The function g is defined for all nonzero x by the equation g (x) = x^{3} - \frac{1}{x ^{3}} . If x is not equal to 0, which of the following equals g (\frac{1}{x}) ?

Explanation	Calculations	Help
$We substitute \frac{1}{x} into the definition of g .$	$g (\frac{1}{x}) = (\frac{1}{x})^{3} - \frac{1}{( \frac{1}{x} ) ^{3}}$	Theory & Tactics Method Card ALG5-A Click to view full details
$We simplify each power and reciprocal.$	$g (\frac{1}{x}) = \frac{1}{x ^{3}} - x^{3}$
$We factor out a negative to match the original function form.$	$\frac{1}{x ^{3}} - x^{3} = - (x^{3} - \frac{1}{x ^{3}}) = - g (x)$
$We verify that g (- x) also equals this same expression.$	$g (- x) = (- x)^{3} - \frac{1}{( - x ) ^{3}} = - x^{3} + \frac{1}{x ^{3}} = - (x^{3} - \frac{1}{x ^{3}}) = - g (x)$

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B