QuestionFind composite functions for $f(x)=9x+7$ and $g(x)=x^{2}$: (a) $f \circ g$, (b) $g \circ f$, (c) $f \circ f$, (d) $g \circ g$. State their domains.

Studdy Solution
The domain of $g \circ g$ is also all real numbers, since there are no restrictions on $x$ in the equation $(x^{2})^{2}$.
In conclusion, the composite functions and their domains are(a) $(f \circ g)(x)=9x^{2}+7$, domain is all real numbers. (b) $(g \circ f)(x)=(9x+7)^{2}$, domain is all real numbers. (c) $(f \circ f)(x)=9(9x+7)+7$, domain is all real numbers. (d) $(g \circ g)(x)=(x^{2})^{2}$, domain is all real numbers.