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1 . The functions $f : \mathbb{N}^2 \rightarrow \mathbb{N}$ and $g : \mathbb{N} \rightarrow \mathbb{N}$ are recursively defined as follows:
$f(m, 0)$ $= m\ \;$ $\mathrm{if}\ m \geq 0,$
$f(m, n)$ $= 1 + f(m, n - 1)\ \;$ $\mathrm{if}\ m \geq 0$ $\mathrm{and}\ n \geq 1,$
$g(0)$ $= 1,$
$g(n)$ $= 5 \cdot g(n - 1)\ \;$ $\mathrm{if}\ n \geq 1.$
For any integer $n \geq 0$, what is $f(g(n), g(n))$?
(a)
$2 \cdot 5^{n-1}$
(b)
$(5^{n})^{2}$
(c)
$2 \cdot 5^{n}$
(d)
$(5^{n-1})^{2}$