Perform the requested operation or operations. Find the domain of each.
-$f ( x ) = \sqrt { 6 x + 6 } , g ( x ) = \sqrt { 6 x - 6 }$ Find $( f + g ) ( x )$
A) $\sqrt { 12 x }$; domain: $[ 0 , \infty )$
B) $x \sqrt { 12 }$; domain: $( - \infty , \infty )$
C) $6 x$; domain: $( - \infty , \infty )$
D) $\sqrt { 6 x + 6 } + \sqrt { 6 x - 6 }$; domain: $[ 1 , \infty )$

Question

Quizplus · Accepted Answer

The domain of $f(x) = \sqrt{6x + 6}$ is $x \geq -1$ and the domain of $g(x) = \sqrt{6x - 6}$ is $x \geq 1$. When adding $f(x)$ and $g(x)$, the combined domain is the intersection of their individual domains, which is $x \geq 1$, or $[1, \infty)$. The expression for $(f + g)(x)$ is simply the sum of $f(x)$ and $g(x)$, which is $\sqrt{6x + 6} + \sqrt{6x - 6}$.

Perform the Requested Operation or Operations f(x)=6x+6,g(x)=6x−6f ( x ) = \sqrt { 6 x + 6 } , g ( x ) = \sqrt { 6 x - 6 }f(x)=6x+6​,g(x)=6x−6​

Perform the Requested Operation or Operations $f ( x ) = \sqrt { 6 x + 6 } , g ( x ) = \sqrt { 6 x - 6 }$