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) $\left(\frac{f}{g}\right)(x)$

Answer

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Answer

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

Steps

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 $x = 0$.