Given f(x) = x^2, g(x) = x + 7 Find (f @ g)(x). Find the domain of (f @ g)(x). Find (g @ f)(x). Find the domain of (g @ f)(x). Find (f @ f)(x). Find the domain of (f @ f)(x). Find (g @ g)(x). Find the domain of (g @ g)(x).

${\displaystyle f\circ g\left(x\right)=f\left(g\left(x\right)\right)={\left(g\left(x\right)\right)}^2={(x+7)}^2}$
${\displaystyle =x^2+14x+49}$
It is a polunomial so domain is all real numbers
Domain of ${\displaystyle f\circ g\left(x\right)}$ is ${\displaystyle (-\mathrm{\infty },\mathrm{\infty })}$
${\displaystyle g\circ f\left(x\right)=f\left(x\right)+7=x^2+7}$
It is a polunomial so domain is all real numbers
Domain of ${\displaystyle g\circ f\left(x\right)}$ is ${\displaystyle (-\mathrm{\infty },\mathrm{\infty })}$
${\displaystyle f\circ f\left(x\right)={\left(f\left(x\right)\right)}^2={\left(x^2\right)}^2=x^4}$
It is a polunomial so domain is all real numbers
Domain of ${\displaystyle f\circ f\left(x\right)}$ is ${\displaystyle (-\mathrm{\infty },\mathrm{\infty })}$
${\displaystyle g\circ g\left(x\right)=g\left(x\right)+7=x+7+7=x+14}$
It is a polunomial so domain is all real numbers
Domain of ${\displaystyle g\circ g\left(x\right)}$ is ${\displaystyle (-\mathrm{\infty },\mathrm{\infty })}$