Find functions f and g so that f ° g = H.
-$$H ( x ) = \left( 5 - 2 x ^ { 3 } \right) ^ { 2 }$$
A) $f ( x ) = 5 - 2 x ^ { 3 } ; g ( x ) = x ^ { 2 }$
B) $f ( x ) = x ^ { 2 } ; g ( x ) = 5 - 2 x ^ { 3 }$
C) $f ( x ) = ( 5 - 2 x ) ^ { 3 } ; g ( x ) = x ^ { 2 }$
D) $f ( x ) = x ^ { 3 } ; g ( x ) = ( 5 - 2 x ) ^ { 2 }$

Question

Quizplus · Accepted Answer

The correct choice is B because $f(g(x)) = f(5 - 2x^3) = (5 - 2x^3)^2$ matches the given function $H(x)$. Here, $g(x)$ performs the inner operation $5 - 2x^3$, and then $f(x) = x^2$ squares the result, exactly as $H(x)$ does.

Find Functions F and G So That F ° G H(x)=(5−2x3)2H ( x ) = \left( 5 - 2 x ^ { 3 } \right) ^ { 2 }H(x)=(5−2x3)2

Find Functions F and G So That F ° G $H ( x ) = \left( 5 - 2 x ^ { 3 } \right) ^ { 2 }$