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Q)

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

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A)
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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 $x=-3, \; \lim\limits_{x\to -3} f(x) = \lim\limits_{x\to -3} 5x-3 = 5 \times -3 - 3 = -15-3 = -18$
$f(-3) = 5 \times -3 - 3 =-15-3=-18$
Since $\lim\limits_{x\to -3} f(x) = f(-3)$, $f(x)$ is continous at $x=-3$.
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