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If $f:[-3,4] \rightarrow R, f(x)=2 x$, and $g:[-2,6] \rightarrow R, g(x)=x^2$. Then find function $(f+g)(x)$.
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The correct answer is:
$(f+g)(x)=2 x+x^2$
$f \longrightarrow:[-3,4] \rightarrow R, f(x)=2 x$, and $g:[-2,6] \rightarrow R, g(x)=x^2$
For $(f+g)(x)$ we consider common domain of $f(x)$ and $g(x)$.
Now $[-3,4] \cap[-2,6] \equiv[-2,4]$
So, $(f+g):[-2,4] \rightarrow R,(f+g)(x)=2 x+x^2$.
For $(f+g)(x)$ we consider common domain of $f(x)$ and $g(x)$.
Now $[-3,4] \cap[-2,6] \equiv[-2,4]$
So, $(f+g):[-2,4] \rightarrow R,(f+g)(x)=2 x+x^2$.
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