Examine the continuity of the function f(x) = 2x^2 – 1 at x = 3. - Vidyadip

Question

Examine the continuity of the function $f(x) = 2x^2 – 1$ at $x = 3.$

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Answer

Here $f(x) = 2x^2 - 1$
$^{\ \ \text{Lt}}_{\text{x}\rightarrow{3}}\text{f(x)}=^{\ \ \text{Lt}}_{\text{x}\rightarrow{3}}(2\text{x}^3-1) = 2(3)^2 - 1$
$= 2(9) - 1 = 18 - 1 = 17$
Now $f$ is defined at $x = 3$
and $f(x) = 2(3)^2 - 1 = 2(9) - 1 = 18 - 1 = 17$
$\therefore\ \ \text{Lt}\ \ \ \ \text{f(x)} = \text{f(3)} = 17$
$\ \ \ \ \text{x}\rightarrow3$
$\therefore f$ is continous at $x = 3.$

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