The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except -3 Which of the following describes the domain of (gcirc f)(x) all real values except xneq -3 and the x for which f(x)neq 7 all real values except xneq -3 and the x for which f(x)neq -3 all real values except xneq 7 and the x for which f(x)=7 all real values except xneq 7 and the x for which f(x)neq -3

To find the domain of $(g\circ f)(x)$, we need to consider the domains of both $f(x)$ and $g(x)$.<br /><br />The domain of $f(x)$ is the set of all real values except 7. This means that $f(x)$ is defined for all real values of $x$ except when $x = 7$.<br /><br />The domain of $g(x)$ is the set of all real values except $-3$. This means that $g(x)$ is defined for all real values of $x$ except when $x = -3$.<br /><br />When we compose $g$ with $f$, we need to ensure that the output of $f(x)$ is within the domain of $g(x)$. In other words, we need to find the values of $x$ for which $f(x) \neq -3$.<br /><br />Therefore, the domain of $(g\circ f)(x)$ is the set of all real values except $x\neq 7$ and the $x$ for which $f(x)\neq -3$.<br /><br />So, the correct answer is: all real values except $x\neq 7$ and the $x$ for which $f(x)\neq -3$.