Answer
$f+g=3x$
The domain is $(-\infty,\infty)$
$f-g=-x$
The domain is $(-\infty,\infty)$
$fg=2x^{2}$
The domain is $(-\infty,\infty)$
$f/g=\dfrac{1}{2}$
The domain is $(-\infty,\infty)$
Work Step by Step
$f(x)=x$ $;$ $g(x)=2x$
Evaluate the combinations and simplify if possible. Then find the domain of the resulting function:
$f+g$
$f(x)+g(x)=x+2x=3x$
This function is defined for all real numbers. The domain is $(-\infty,\infty)$
$f-g$
$f(x)-g(x)=x-2x=-x$
This function is defined for all real numbers. The domain is $(-\infty,\infty)$
$fg$
$f(x)\cdot g(x)=(x)(2x)=2x^{2}$
This function is defined for all real numbers. The domain is $(-\infty,\infty)$
$f/g$
$\dfrac{f(x)}{g(x)}=\dfrac{x}{2x}=\dfrac{1}{2}$
This function is defined for all real numbers. The domain is $(-\infty,\infty)$
