b. the domain of $(g \circ f)(x)$ in interval notation. Enter the exact answer. To enter $\infty$, type infinity. To enter $U$, type U. Domain:

Step 1 ：For the function \((g \circ f)(x)\), the inner function is \(f(x)\) and the outer function is \(g(x)\). The domain of \(f(x)\) is all real numbers. After applying the outer function \(g(x)\), the domain is all real numbers except those for which \(f(x) = -3\). This happens when \(x^{2}-7 = -3\), or \(x^{2} = 4\), which gives \(x = -2\) or \(x = 2\).

Step 2 ：The domain of \((g \circ f)(x)\) is \(\boxed{(-\infty, -2) \cup (-2, 2) \cup (2, \infty)}\).