Question

Given, $f\left(x\right)=1-|x-2|$ for $1\le x\le 3$ and $f\left(3x\right)=af\left(x\right)$ for all other values of $x$. If $a=3$, then $\underset{x\to {10}^{+}}{lim}f\left(x\right)=?$ and $\underset{x\to {10}^{-}}{lim}f\left(x\right)=?$

Answer 1

$f\left(x\right)=1-|x-2|$

${lim}_{x\to {10}^{+}}f\left(x\right)$

$={lim}_{x\to {10}^{+}}(1-|x-2|)$

$={lim}_{x\to {10}^{+}}(3-x)$

$=3-10=-7$

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${lim}_{x\to {10}^{-}}f\left(x\right)$

$={lim}_{x\to {10}^{-}}(1-|x-2|)$

$={lim}_{x\to {10}^{-}}(3-x)$

$=3-10=-7$