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

Answer

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Answer

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

Steps

Step 1 ： $(f + g) (x) = f (x) + g (x) = 7 x + 2 x^{2}$

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

Step 3 ： $(f - g) (x) = f (x) - g (x) = 7 x - 2 x^{2}$

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

Step 5 ： $(f g) (x) = f (x) * g (x) = 14 x^{3}$

Step 6 ：The domain of $(f g) (x)$ is all real numbers.

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

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