For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = \frac { 5 x - 8 } { 9 x - 2 } ; g ( x ) = \frac { 3 x } { 9 x - 2 }$ Find f - g.
A) $( f - g ) ( x ) = \frac { 2 x - 8 } { 9 x - 2 } ; \left\{ x \mid x \neq \frac { 2 } { 9 } , x \neq 4 \right\}$
B) $( f - g ) ( x ) = \frac { 2 x - 8 } { 9 x - 2 } ; \left\{ x \mid x \neq \frac { 2 } { 9 } \right\}$
C) $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \frac { 8 \mathrm { x } + 8 } { 9 \mathrm { x } - 2 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 2 } { 9 } \right\}$
D) $( f - g ) ( x ) = \frac { 2 x - 8 } { 9 x - 2 } ; \{ x \mid x \neq 0 \}$

Question

For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = \frac { 5 x - 8 } { 9 x - 2 } ; g ( x ) = \frac { 3 x } { 9 x - 2 }$ Find f - g. 
A) $( f - g ) ( x ) = \frac { 2 x - 8 } { 9 x - 2 } ; \left\{ x \mid x \neq \frac { 2 } { 9 } , x \neq 4 \right\}$
B) $( f - g ) ( x ) = \frac { 2 x - 8 } { 9 x - 2 } ; \left\{ x \mid x \neq \frac { 2 } { 9 } \right\}$
C) $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \frac { 8 \mathrm { x } + 8 } { 9 \mathrm { x } - 2 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 2 } { 9 } \right\}$
D) $( f - g ) ( x ) = \frac { 2 x - 8 } { 9 x - 2 } ; \{ x \mid x \neq 0 \}$

Quizplus · Accepted Answer

To find $f - g$, subtract $g(x)$ from $f(x)$: $f(x) - g(x) = \frac{5x - 8}{9x - 2} - \frac{3x}{9x - 2} = \frac{5x - 8 - 3x}{9x - 2} = \frac{2x - 8}{9x - 2}$. The domain excludes values that make the denominator zero, which is only $x = \frac{2}{9}$.

For the Given Functions F and G, Find the Requested f(x)=5x−89x−2;g(x)=3x9x−2f ( x ) = \frac { 5 x - 8 } { 9 x - 2 } ; g ( x ) = \frac { 3 x } { 9 x - 2 }f(x)=9x−25x−8​;g(x)=9x−23x​

For the Given Functions F and G, Find the Requested $f ( x ) = \frac { 5 x - 8 } { 9 x - 2 } ; g ( x ) = \frac { 3 x } { 9 x - 2 }$