Find $( f g ) ( x )$.
$$f ( x ) = \sqrt { - 5 x } \quad g ( x ) = \sqrt { - 8 x + 6 }$$
A) $( f g ) ( x ) = 2 x \sqrt { 10 } - \sqrt { 30 x }$
B) $( f g ) ( x ) = 2 x \sqrt { 10 - 30 x }$
C) $( f g ) ( x ) = \sqrt { - 13 x + 6 }$
D) $( f g ) ( x ) = \sqrt { 40 x ^ { 2 } + 6 }$
E) $( f g ) ( x ) = \sqrt { 40 x ^ { 2 } - 30 x }$

Question

Quizplus · Accepted Answer

To find $(fg)(x)$, we substitute $g(x)$ into $f(x)$, resulting in $f(g(x)) = \sqrt{-5(\sqrt{-8x + 6})}$. However, this simplification is incorrect. The correct approach is to apply $f$ to $g(x)$ directly, which means we should compute $f(g(x))$ correctly. Since there's a misunderstanding in the simplification process, let's correct the approach: $(fg)(x) = f(g(x)) = \sqrt{-5(\sqrt{-8x + 6})}$ is not the right interpretation of function composition here. Instead, we should apply $g(x)$ into $f(x)$ correctly, but the provided explanation mistakenly suggests an incorrect substitution and simplification process. The correct process involves substituting $g(x)$ into $f(x)$ properly, which actually means calculating $f(g(x))$ as $f(\sqrt{-8x + 6})$, but this explanation does not directly lead to any of the given options correctly due to a misinterpretation of how to perform function composition. The correct method involves calculating the composition of $f$ and $g$ without the incorrect substitution error, leading to the correct answer by properly applying the definition of function composition.

Find (fg)(x)( f g ) ( x )(fg)(x) f(x)=−5xg(x)=−8x+6f ( x ) = \sqrt { - 5 x } \quad g ( x ) = \sqrt { - 8 x + 6 }f(x)=−5x​g(x)=−8x+6​

Find $( f g ) ( x )$ $f ( x ) = \sqrt { - 5 x } \quad g ( x ) = \sqrt { - 8 x + 6 }$