Find functions f and g so that f ° g = H.
-$$H ( x ) = | 3 x + 7 |$$
A) $f ( x ) = x ; g ( x ) = 3 x + 7$
B) $f ( x ) = | x |$;
$g ( x ) = 3 x + 7$
C) $f ( x ) = | - x | ; \quad g ( x ) = 3 x - 7$
D) $f ( x ) = - | x | ; \quad g ( x ) = 3 x + 7$

Question

Quizplus · Accepted Answer

The correct choice is B because $f ( x ) = | x |$ takes the absolute value of its input, and $g ( x ) = 3 x + 7$ is the linear function inside the absolute value in $H(x)$. Thus, $f(g(x)) = |3x + 7| = H(x)$.

Find Functions F and G So That F ° G H(x)=∣3x+7∣H ( x ) = | 3 x + 7 |H(x)=∣3x+7∣

Find Functions F and G So That F ° G $H ( x ) = | 3 x + 7 |$