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]
