Question

The domain of f(x)=log {(x - 3)(6-x)} is
1) (3,60) 2) (3,6) 3) (0,00) 4)(-00,00)​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

The domain of the function

$\sf{ f(x) = \log (x - 3)(6 - x)\: \: }$

CALCULATION

Here

$\sf{ f(x) = \log (x - 3)(6 - x)\: \: }$

Now the given function f(x) is well defined when

$\sf{ \log (x - 3)(6 - x)\: \: \: is \: \: well \: defined \: }$

$\implies \: \sf{ (x - 3)(6 - x)\: > 0 \: }$

$\implies \: \sf{ 3 < x < 6 \: }$

Hence the domain of the function is

$= \sf{ \{ \: x \in \mathbb{ R\: } : \: 3 < x < 6\: \}}$

$= \sf{ ( \: 3 , \: 6 \: )}$

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