The function f is defined for all nonzero x by the equation f(x)=x-1/x If x...

Question

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

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B. f(1/x) equals f(-x) We substitute 1/x into the definition of f. f(1/x)=1/x-11/x We simplify the reciprocal of a reciprocal to the original value. f(1/x)=1/x-x We factor out a negative to match the original function form. 1/x-x=-(x-1/x) =-f(x) We verify that f(-x) also equals this same expression. f(-x)=-x-1/-x =-x+1/x =-(x-1/x) =-f(x)

Explanation	Calculations	Help
$We substitute \frac{1}{x} into the definition of f .$	$f (\frac{1}{x}) = \frac{1}{x} - \frac{1}{\frac{1}{x}}$
$We simplify the reciprocal of a reciprocal to the original value.$	$f (\frac{1}{x}) = \frac{1}{x} - x$
$We factor out a negative to match the original function form.$	$\frac{1}{x} - x = - (x - \frac{1}{x}) = - f (x)$
$We verify that f (- x) also equals this same expression.$	$f (- x) = - x - \frac{1}{- x} = - x + \frac{1}{x} = - (x - \frac{1}{x}) = - f (x)$

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