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  4. The domain of the function f given by f(x) = (x2+2x+1/x2-x-6) is

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Q. The domain of the function $f$ given by $f\left(x\right) = \frac{x^{2}+2x+1}{x^{2}-x-6}$ is

Relations and Functions

Solution:

Given, $f\left(x\right) = \frac{x^{2}+2x+1}{x^{2}-x-6}$
For domain of $f\left(x\right)$, $x^{2} - x - 6 \ne 0$
$\therefore \left(x-3\right)\left(x + 2 \right)\ne0$
$\Rightarrow x \ne 3, -2$
$\therefore $ Domain of $f\left(x\right)$ is $R - \left\{3, -2\right\}$.