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Properties of Inequalities

Find the doma...

Question

Find the domain of the function $f (x) = \frac{x^{2} + 3 x + 5}{x^{2} - 5 x + 4}$

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Solution

Given $f (x) = \frac{x^{2} + 3 x + 5}{x^{2} - 5 x + 4}$
$f (x)$ is defined for all real numbers except $x^{2} - 5 x + 4 = 0$
But $x^{2} - 5 x + 4 = (x - 4) (x - 1)$
Domain of $f = R - {1, 4}$

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