Find functions f and g so that f $f \circ g = H$
-$$H ( x ) = \left| 4 - 3 x ^ { 2 } \right|$$
A) $f ( x ) = 4 - 3 x ^ { 2 } ; g ( x ) = | x |$
B) $f ( x ) = x ^ { 2 } ; g ( x ) = 4 - 3 | x |$
C) $f ( x ) = 4 - 3 | x | ; g ( x ) = x ^ { 2 }$
D) $f ( x ) = | x | ; g ( x ) = 4 - 3 x ^ { 2 }$

Question

Quizplus · Accepted Answer

The correct functions are $f(x) = |x|$ and $g(x) = 4 - 3x^2$. When $g(x)$ is applied first, it transforms $x$ into $4 - 3x^2$, and then applying $f(x)$ takes the absolute value of that result, matching $H(x) = |4 - 3x^2|$.

Find Functions F and G So That F f∘g=Hf \circ g = Hf∘g=H

Find Functions F and G So That F $f \circ g = H$