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

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

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

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B. f (1/ x) equals f (- x)

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

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

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B. f (1/ x) equals f (- x)