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For which of the following functions are both the original function and its inverse increasing for all $x \ne 0$?

I. $ f( x ) =\sqrt { |x|} $II. $ f( x ) =- \cfrac {1}{x}$III. $ f( x ) ={ x }^{ \frac{1}{3}}$

I only.

II only.

II and III only.

I, II, and III.