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Geometric Interpretation of Def.Int as Limit of Sum

Find the doma...

Question

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

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Solution

For
$\sqrt{4 x - x^{2}} 4 x - x^{2} \geq 0 x^{2} - 4 x \leq 0 x (x - 4) \leq 0 x \in [0, 4]$

For
${log}_{3} (x - 2) x - 2 > 0 x > 2$

Taking intersection,
$x \in (2, 4]$

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