Find functions f and g so that f ° 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 choice is D because $f(g(x)) = |4 - 3x^2|$ matches the given $H(x)$ when $f(x) = |x|$ and $g(x) = 4 - 3x^2$. This means $f$ takes the absolute value of whatever $g$ outputs, which is exactly how $H(x)$ is defined.

Find Functions F and G So That F ° G H(x)=∣4−3x2∣H ( x ) = \left| 4 - 3 x ^ { 2 } \right|H(x)=​4−3x2​

Find Functions F and G So That F ° G $H ( x ) = \left| 4 - 3 x ^ { 2 } \right|$