Find $g \circ g \circ g$, where $g ( x ) = x ^ { 2 }$.
A) $x ^ { 6 }$
B) $6 x ^ { 6 }$
C) $8 x ^ { 8 }$
D) $x ^ { 8 }$
E) $x ^ { 8 } + 8$

Question

Quizplus · Accepted Answer

$g \circ g ( x ) = g ( g ( x )) = g ( x ^ { 2 } ) = ( x ^ { 2 } ) ^ { 2 } = x ^ { 4 }$.

Therefore, $g \circ g \circ g ( x ) = g ( g \circ g ( x )) = g ( x ^ { 4 } ) = ( x ^ { 4 } ) ^ { 2 } = x ^ { 8 }$.

The correct answer is (D), and none of the other options match this result.

Find g∘g∘gg \circ g \circ gg∘g∘g , Where g(x)=x2g ( x ) = x ^ { 2 }g(x)=x2