Problem

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

Solution

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 \(x = 0\).

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Source: https://solvelyapp.com/problems/kBgJfBrv2W/

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