QuestionFind the composite functions for $f(x)=2x+3$ and $g(x)=x^{2}$ and state their domains: (a) $f \circ g$, (b) $g \circ f$, (c) $f \circ f$, (d) $g \circ g$.

Studdy Solution
The domain of the function $g \circ g$ is all real numbers because there are no restrictions on the values of $x$ that can be squared and then squared again.
In conclusion, the composite functions and their domains are(a) $(f \circ g)(x) =2x^{2} +3$, domain all real numbers(b) $(g \circ f)(x) = (2x+3)^{2}$, domain all real numbers(c) $(f \circ f)(x) =4x +9$, domain all real numbers(d) $(g \circ g)(x) = x^{4}$, domain all real numbers