Let $f(x)=7 x$ and $g(x)=2 x^{2}$. Find a formula for each of the following expressions. Find their domains. (a) $(\mathrm{f}+\mathrm{g})(\mathrm{x})$ (b) $(f-g)(x)$ (c) $(\mathrm{fg})(\mathrm{x})$ (d) $\left(\frac{f}{g}\right)(x)$

Step 1 ：\((f+g)(x) = f(x) + g(x) = 7x + 2x^2\)

Step 2 ：The domain of \((f+g)(x)\) is all real numbers.

Step 3 ：\((f-g)(x) = f(x) - g(x) = 7x - 2x^2\)

Step 4 ：The domain of \((f-g)(x)\) is all real numbers.

Step 5 ：\((fg)(x) = f(x) * g(x) = 14x^3\)

Step 6 ：The domain of \((fg)(x)\) is all real numbers.

Step 7 ：\(\left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} = \frac{7}{2x}\)

Step 8 ：The domain of \(\left(\frac{f}{g}\right)(x)\) is all real numbers except \(x = 0\).