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

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

Explanation	Calculations	Help
$We substitute \frac{1}{z} into the definition of h .$	$h (\frac{1}{z}) = \frac{1}{z} + \frac{1}{\frac{1}{z}}$	Theory & Tactics Method Card ALG5-A Click to view full details
$We simplify the reciprocal of a reciprocal to the original value.$	$h (\frac{1}{z}) = \frac{1}{z} + z$
$We observe that this matches the original function form.$	$\frac{1}{z} + z = z + \frac{1}{z} = h (z)$

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A

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

Explanation	Calculations	Help
$We substitute \frac{1}{z} into the definition of h .$	$h (\frac{1}{z}) = \frac{1}{z} + \frac{1}{\frac{1}{z}}$	Theory & Tactics Method Card ALG5-A Click to view full details
$We simplify the reciprocal of a reciprocal to the original value.$	$h (\frac{1}{z}) = \frac{1}{z} + z$
$We observe that this matches the original function form.$	$\frac{1}{z} + z = z + \frac{1}{z} = h (z)$

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A