Answer
$f+g=2x^{2}+x$
The domain is $(-\infty,\infty)$
$f-g=x$
The domain is $(-\infty,\infty)$
$fg=x^{4}+x^{3}$
The domain is $(-\infty,\infty)$
$f/g=\dfrac{x^{2}+x}{x^{2}}$
The domain is $(-\infty,0)\cup(0,\infty)$ or $\{x|x\ne0\}$
Work Step by Step
$f(x)=x^{2}+x$ $;$ $g(x)=x^{2}$
Evaluate the combinations and simplify if possible. Then , find the domains of the resulting functions:
$f+g$
$f(x)+g(x)=(x^{2}+x)+(x^{2})=2x^{2}+x$
This function is defined for all real numbers. The domain is $(-\infty,\infty)$
$f-g$
$f(x)-g(x)=(x^{2}+x)-(x^{2})=x$
This function is defined for all real numbers. The domain is $(-\infty,\infty)$
$fg$
$f(x)\cdot g(x)=(x^{2}+x)(x^{2})=x^{4}+x^{3}$
This function is defined for all real numbers. The domain is $(-\infty,\infty)$
$f/g$
$\dfrac{f(x)}{g(x)}=\dfrac{x^{2}+x}{x^{2}}$
This function is undefined for all the values of $x$ that make the denominator equal to $0$. To find these values, set the denominator equal to $0$ and solve the equation:
$x^{2}=0$
$x=0$
The domain is $(-\infty,0)\cup(0,\infty)$ or $\{x|x\ne0\}$
