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Is the function $f (x) = 5x – 3$ continuous at $x=5$?

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  • If $f$ is a real function on a subset of the real numbers and $c$ a point in the domain of $f$, then $f$ is continous at $c$ if $\lim\limits_{x\to c} f(x) = f(c)$.
Given $f(x) = 5x-3$.
At $x=-3, \; \lim\limits_{x\to 5} f(x) = \lim\limits_{x\to 5} 5x-3 = 5 \times 5 - 3 = 25-3 = 22$
$f(5) = 5 \times 5 - 3 =25-3 = 22$
Since $\lim\limits_{x\to 5} f(x) = f(5)$, $f(x)$ is continous at $x=5$.
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