QuestionFind $f \circ g$ and $g \circ f$ for $f(x)=\sqrt{x+8}$ and $g(x)=x^{2}$. Determine the domains in interval notation.

Studdy Solution
olve for $x$.
$$x \geq -8$$So the domain of $g \circ f(x)$ is $[-8, \infty)$.
In conclusion, we have(a) $f \circ g(x) = \sqrt{x^{2}+8}$ with domain $(-\infty, \infty)$(b) $g \circ f(x) = x+8$ with domain $[-8, \infty)$The domain of $f(x)$ is $[-8, \infty)$ and the domain of $g(x)$ is $(-\infty, \infty)$.