Check the continuity of the function f given by f(x) = 2x + 3 at … - Vidyadip

Question

Check the continuity of the function f given by f(x) = 2x + 3 at x = 1.

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Answer

First of all note that the function is defined at the given point x = 1 and f(1) = 5.
Clearly
$\mathop {\lim }\limits_{x \to 1} f(x) = \mathop {\lim }\limits_{x \to 1} $ (2x + 3) = 2(1) + 3 = 5
Thus $\mathop {\lim }\limits_{x \to 1} f(x)$ = 5 = f (1)
Hence, f is continuous at x = 1.

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