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Given that f(x)=x'2−12x and g(x)=x+12, find(a) (f+g)(x)=(b) (f−g)(x)=c) (fg)(x)= (d) (f/g)(x)=

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Sagot :

Given:

[tex]\begin{gathered} f(x)=x^2-12x \\ g(x)=x+12 \end{gathered}[/tex]

Required:

To find

[tex]\begin{gathered} (f+g)(x) \\ (f-g)(x) \\ (fg)(x) \\ (\frac{f}{g})(x) \end{gathered}[/tex]

Explanation:

Now

[tex]\begin{gathered} (f+g)(x)=f(x)+g(x) \\ =x^2-12x+x+12 \\ =x^2-11x+12 \end{gathered}[/tex][tex]\begin{gathered} (f-g)(x)=f(x)-g(x) \\ =x^2-12x-x-12 \\ =x^2-13x-12 \end{gathered}[/tex][tex]\begin{gathered} (fg)(x)=f(x)g(x) \\ =(x^2-12x)(x+12) \\ =x^3+12x^2-12x^2-144x \\ =x^3-144x \end{gathered}[/tex][tex]\begin{gathered} (\frac{f}{g})(x)=\frac{f(x)}{g(x)} \\ \\ =\frac{x^2-12x}{x+12} \end{gathered}[/tex]

Final Answeer:

[tex]\begin{gathered} (f+g)(x)=x^2-11x+12 \\ (f-g)(x)=x^2-13x-12 \\ (fg)(x)=x^3-144x \\ (\frac{f}{g})(x)=\frac{x^2-12x}{x+12} \end{gathered}[/tex]

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