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

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Solution

The function is continuous at $x = 1$ if ${lim}_{x \to 1} f (x) = f (1)$

L.H.S $= {lim}_{x \to 1} f (x)$

$= {lim}_{x \to 1} (2 x + 3) = 2 \times 1 + 3 = 2 + 3 = 5$

R.H.S $= f (1) = 2 \times 1 + 3 = 2 + 3 = 5$

Since L.H.S $=$ R.H.S

$∴$ the function is continuous.

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