QuestionFind $(a)(f \circ g)(x)$ and its domain, and $(b)(g \circ f)(x)$ and its domain for $f(x)=\sqrt{x}, g(x)=x+3$.

Studdy Solution
The domain of $(g \circ f)(x)$ is all $x$ such that $x \geq0$, because the radicand (the value under the square root) must be greater than or equal to zero.
So, $(a)(f \circ g)(x)=\sqrt{x+3}$ with domain $x \geq -3$, and $(b)(g \circ f)(x)=\sqrt{x}+3$ with domain $x \geq0$.