Examine the continuity of : f(x)=x^2-9 x-3 on R - Vidyadip

Question

Examine the continuity of : $\mathrm{f}(\mathrm{x})=\frac{x^2-9}{x-3}$ on $\mathrm{R}$

✓

Answer

$
f(x)=\frac{x^2-9}{x-3} ; x \in R
$
$f(x)$ is a rational function and is continuous for all $x \in R$, except at the points where denominator becomes zero.
Here, denominator $x-3=0$ when $x=3$.
$\therefore$ Function $\mathrm{f}$ is continuous for all $\mathrm{x} \in \mathrm{R}$, except at $\mathrm{x}=3$, where it is not defined.

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