Let \( f(x)=\left\{\begin{array}{cc}a x+b, & \text { if } x1 \\ 3 b x-2 a+1, & \text { if } x1\e...

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Let \( f(x)=\left\{\begin{array}{cc}a x+b, & \text { if } x1 \\ 3 b x-2 a+1, & \text { if } x1\end{array}\right. \).
Find a relation between \( a \) and \( b \) so that \( \operatorname{Lim}_{x \rightarrow 1} f(x) \) exists.
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