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  4. Domain of the function f(x)= log (√x-4+ √6-x) is

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Q. Domain of the function $ f(x)=\log (\sqrt{x-4}+ $ $ \sqrt{6-x}) $ is

Rajasthan PETRajasthan PET 2001

Solution:

$ f(x)=\log (\sqrt{x-4}+\sqrt{6-x}) $
$ \sqrt{x-4}\ge 0,\sqrt{6-x}\ge 0 $
$ \Rightarrow $ $ x-4\ge 0,6-x\ge 0 $
$ \Rightarrow $ $ x\ge 4,x\le 6 $
$ \therefore $ Domain is [4, 6]