Answer
$7$
Work Step by Step
Given $\lim\limits_{x \to 4}\frac{f(x)-5}{x-2}=1$, we have $\frac{\lim\limits_{x \to 4}f(x)-5}{4-2}=1$ thus $\lim\limits_{x \to 4}f(x)=(4-2)+5=7$
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