For the functions $f(x)=\frac{x}{x+3}$ and $g(x)=\frac{7}{x}$, find the composition $f g$ and simplify your answer as much as possible. Write the domain using interval notation. \[ (f \circ g)(x)=\square \] Domain of $f \circ g: \square$ \begin{tabular}{|c|c|c|} \hline 믐 & $\square^{\square}$ & $\sqrt{\square}$ \\ \hline 미미 & $(\square, \square)$ & {$[\square, \square]$} \\ \hline & $(\square, \square]$ & {$[\square, \square)$} \\ \hline$\varnothing$ & $\infty$ & $-\infty$ \\ \hline$x$ & & 6 \\ \hline \end{tabular} Explanation Check 0 2023 McGraw HillLC. Al Rights Resenved. Terms of Use I Pivogy Cente

Step 1 ：Substitute \(g(x)\) into \(f(x)\) to get \(f(g(x)) = f\left(\frac{7}{x}\right) = \frac{\frac{7}{x}}{\frac{7}{x} + 3}\)

Step 2 ：Multiply the numerator and the denominator by \(x\) to simplify the expression: \(f(g(x)) = \frac{7}{7 + 3x}\)

Step 3 ：Set the denominator equal to zero and solve for \(x\) to find the domain: \(7 + 3x = 0\) gives \(x = -\frac{7}{3}\)

Step 4 ：The domain of \(f(g(x))\) is all real numbers except \(-\frac{7}{3}\). In interval notation, this is \((-\infty, -\frac{7}{3}) \cup (-\frac{7}{3}, \infty)\)

Step 5 ：\(\boxed{(f \circ g)(x) = \frac{7}{7 + 3x}}\)

Step 6 ：\(\boxed{\text{Domain of } f \circ g: (-\infty, -\frac{7}{3}) \cup (-\frac{7}{3}, \infty)}\)