Find ( fg )(x). $f ( x ) = \sqrt { 3 x } \quad g ( x ) = \sqrt { 5 x + 7 }$
A) $( f g ) ( x ) = \sqrt { 8 x + 7 }$
B) $( f g ) ( x ) = \sqrt { 15 x ^ { 2 } + 7 }$
C) $( f g ) ( x ) = \sqrt { 15 x ^ { 2 } + 21 x }$
D) $( f g ) ( x ) = x \sqrt { 15 } + \sqrt { 21 x }$
E) $( f g ) ( x ) = x \sqrt { 15 + 21 x }$

Question

Quizplus · Accepted Answer

The composition of functions $f(g(x))$ involves substituting $g(x)$ into $f(x)$. Here, $f(x) = \sqrt{3x}$ and $g(x) = \sqrt{5x + 7}$. Substituting $g(x)$ into $f(x)$, we get $f(g(x)) = \sqrt{3(\sqrt{5x + 7})}$. However, the correct operation for finding $(fg)(x)$ is actually multiplying $f(x)$ by $g(x)$, not composing them. Thus, $(fg)(x) = \sqrt{3x} \cdot \sqrt{5x + 7} = \sqrt{3x(5x + 7)} = \sqrt{15x^2 + 21x}$.

Find ( Fg )(X) f(x)=3xg(x)=5x+7f ( x ) = \sqrt { 3 x } \quad g ( x ) = \sqrt { 5 x + 7 }f(x)=3x​g(x)=5x+7​

Find ( Fg )(X) $f ( x ) = \sqrt { 3 x } \quad g ( x ) = \sqrt { 5 x + 7 }$