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:

Answer

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Answer

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

Steps

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 $\boxed{(-\infty, -2) \cup (-2, 2) \cup (2, \infty)}$.

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:

Answer

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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: