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Question

Let $$f(x)=x^2$$ and $$g(x)=2x+1$$ be two real functions. Find $$(f+g)(x),(f-g)(x),(fg)(x), \left(\dfrac{f}{g}\right)(x).$$


Solution

$$(f+g)(x)=f(x)+g(x)$$

$$=x^{2}+2x+1$$

$$(f-g)(x)=f(x)-g(x)$$

$$=x^{2}-(2x+1)$$

$$=x^{2}-2x-1$$

$$(fg)(x)=f(x).g(x)$$

$$=x^{2}\left ( 2x+1 \right )$$

$$=2x^{3}+x^{2}$$

$$\left ( \cfrac{f}{g} \right )(x)=\cfrac{f(x)}{g(x)}$$          $$\left ( \; g(x)\neq 0 \right )$$

$$=\cfrac{x^{2}}{2x+1}$$                         $$\left ( \; x\neq -\cfrac{1}{2} \right )$$


Mathematics

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