For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = \frac { 7 x - 6 } { 6 x - 1 } ; g ( x ) = \frac { 4 x } { 6 x - 1 }$$
Find $f + g$.
A) $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } \right\}$

B) $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \{ x \mid x \neq 0 \}$

C) $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } , x \neq \frac { 6 } { 11 } \right\}$

D) $( f + g ) ( x ) = \frac { 3 x + 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } \right\}$

Question

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = \frac { 7 x - 6 } { 6 x - 1 } ; g ( x ) = \frac { 4 x } { 6 x - 1 }$$
Find $f + g$.
A) $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } \right\}$

B) $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \{ x \mid x \neq 0 \}$

C) $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } , x \neq \frac { 6 } { 11 } \right\}$

D) $( f + g ) ( x ) = \frac { 3 x + 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } \right\}$

Quizplus · Accepted Answer

To find $f + g$, we add the functions $f(x) = \frac{7x - 6}{6x - 1}$ and $g(x) = \frac{4x}{6x - 1}$ together. Since they have the same denominator, we combine the numerators: $7x - 6 + 4x = 11x - 6$. Thus, $f + g = \frac{11x - 6}{6x - 1}$. The domain excludes the value that makes the denominator zero, which is $x = \frac{1}{6}$.

For the Given Functions F and G, Find the Requested f(x)=7x−66x−1;g(x)=4x6x−1f ( x ) = \frac { 7 x - 6 } { 6 x - 1 } ; g ( x ) = \frac { 4 x } { 6 x - 1 }f(x)=6x−17x−6​;g(x)=6x−14x​

For the Given Functions F and G, Find the Requested $f ( x ) = \frac { 7 x - 6 } { 6 x - 1 } ; g ( x ) = \frac { 4 x } { 6 x - 1 }$