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 $(fg)(x)$, you substitute $g(x)$ into $f(x)$, resulting in $f(g(x)) = \sqrt{-5(\sqrt{-8x + 6})}$. However, the correct process involves first applying $g(x)$ and then $f(x)$, which seems to have been misunderstood in the formulation of the question and options provided. The correct approach should involve composing the functions correctly, but based on the options given and the typical interpretation of function composition, none directly match the expected mathematical process. Option E, $\sqrt{40x^2 - 30x}$, could be considered if interpreting the composition as multiplying the insides of the square roots directly, which is not a standard operation for function composition. This appears to be a misunderstanding or misrepresentation of how to correctly compose the functions given.

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