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Variable Separable Method

Find the doma...

Question

Find the domain of definition of the following function:
$y = \sqrt{\frac{1}{2} {log}_{4} 16 - {log}_{8} (x^{2} - 4 x + 3)} .$

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Solution

given equation can be written as $y = \sqrt{1 - l o g_{8} (x^{2} - 4 x + 3)}$
$⟹ 0 < x^{2} - 4 x + 3 < 8$
for $0 < x^{2} - 4 x + 3$ $x \in (- \infty, + \infty) - (1, 3)$
and for $x^{2} - 4 x + 3 < 8$ $x \in (- 1, 5)$
$⟹ x \in (- 1, 1) \cup (3, 5)$

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\begin{matrix} Domain of the function y = \sqrt[4]{\frac{1}{2} {log}_{4} 16 - {log}_{8} (x^{2} - 4 x + 3)} is \end{matrix}

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