 # 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). FobelloE 2020-10-21 Answered
Given
$f\left(x\right)={x}^{2},g\left(x\right)=x+7$
Find $\left(f\circ g\right)\left(x\right).$
Find the domain of $\left(f\circ g\right)\left(x\right).$
Find $\left(g\circ f\right)\left(x\right).$
Find the domain of $\left(g\circ f\right)\left(x\right).$
Find $\left(f\circ f\right)\left(x\right).$
Find the domain of $\left(f\circ f\right)\left(x\right).$
Find $\left(g\circ g\right)\left(x\right).$
Find the domain of $\left(g\circ g\right)\left(x\right).$
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$f\circ g\left(x\right)=f\left(g\left(x\right)\right)={\left(g\left(x\right)\right)}^{2}={\left(x+7\right)}^{2}$
$={x}^{2}+14x+49$
It is a polunomial so domain is all real numbers
Domain of $f\circ g\left(x\right)$ is $\left(-\mathrm{\infty },\mathrm{\infty }\right)$
$g\circ f\left(x\right)=f\left(x\right)+7={x}^{2}+7$
It is a polunomial so domain is all real numbers
Domain of $g\circ f\left(x\right)$ is $\left(-\mathrm{\infty },\mathrm{\infty }\right)$
$f\circ f\left(x\right)={\left(f\left(x\right)\right)}^{2}={\left({x}^{2}\right)}^{2}={x}^{4}$
It is a polunomial so domain is all real numbers
Domain of $f\circ f\left(x\right)$ is $\left(-\mathrm{\infty },\mathrm{\infty }\right)$
$g\circ g\left(x\right)=g\left(x\right)+7=x+7+7=x+14$
It is a polunomial so domain is all real numbers
Domain of $g\circ g\left(x\right)$ is $\left(-\mathrm{\infty },\mathrm{\infty }\right)$