Find the domain of the function f(x) = x^2 + 2x + 1 x^2 - 8x + 12… - Vidyadip

Question

Find the domain of the function $f(x) = \frac{{{x^2} + 2x + 1}}{{{x^2} - 8x + 12}}$.

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Answer

Here $f(x) = \frac{{{x^2} + 2x + 1}}{{{x^2} - 8x + 12}}$
$f (x)$ is a rational function of $x.$
$f (x)$ assumes real values of all x except for those values of $x$ for which
$x^2 - 8x + 12 = 0$
$ \Rightarrow (x - 6)(x - 2) = 0$
$ \Rightarrow x = 2, 6$
$\therefore $ Domain of function $= R - \{2, 6\}.$

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