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

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) $( f g ) ( x ) = \sqrt { 40 x ^ { 2 } - 30 x }$

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 is to multiply the functions, not compose them. The correct operation is $f(x) \cdot g(x) = \sqrt{-5x} \cdot \sqrt{-8x + 6} = \sqrt{40x^2 - 30x}$, which matches choice E.

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