Given $f ( x ) = 2 x + 1$ And $h ( x ) = 2 x ^ { 2 } + 4 x + 1$

Multiple Choice

Given $f ( x ) = 2 x + 1$ and $h ( x ) = 2 x ^ { 2 } + 4 x + 1$ , find a function $g$ such that $f ( g ( x ) ) = h ( x )$

A) $g ( x ) = \left( x ^ { 2 } + 1 \right) ^ { 2 }$
B) $g ( x ) = x ^ { 2 } + 2$
C) $g ( x ) = x ^ { 2 } + 4 x$
D) $g ( x ) = x ^ { 2 } + 2 x$