Let $f(x)=\left\{\begin{array}{l}x-1, x ext { is even, } \ 2 x, \quad x ext { is odd, }\end{array} x \in \mathbf{N} ight.$.
If for some $\mathrm{a} \in \mathbf{N}, f(f(f(\mathrm{a})))=21$, then $\lim\limits_{x ightarrow \mathrm{a}^{-}}\left\{\frac{|x|^3}{\mathrm{a}}-\left[\frac{x}{\mathrm{a}} ight] ight\}$, where $[t]$ denotes the greatest integer less than or equal to $t$, is equal to :

Question

Let $f(x)=\left\{\begin{array}{l}x-1, x 	ext { is even, } \ 2 x, \quad x 	ext { is odd, }\end{array} x \in \mathbf{N}ight.$.
 If for some $\mathrm{a} \in \mathbf{N}, f(f(f(\mathrm{a})))=21$, then $\lim\limits_{x ightarrow \mathrm{a}^{-}}\left\{\frac{|x|^3}{\mathrm{a}}-\left[\frac{x}{\mathrm{a}}ight]ight\}$, where $[t]$ denotes the greatest integer less than or equal to $t$, is equal to :

Accepted Answer

Correct answer: D

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