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Existence of Limit

Find the doma...

Question

Find the domains of definition of the following functions.
$f (x) = l o g_{2 x - 5} (x^{2} - 3 x - 10) .$

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Solution

base must be positive and not equal to 1

therefore $2 x - 5 > 0$ ,x not equal to 3

similarly $x^{2} - 3 x - 10$ >0

for first case solution is x belongs to $(5 / 2, \infty) - 3$

for second case solution is $(- \infty, - 2) \cup (5, \infty)$

therefore the domain is $(5, \infty)$

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