The domain of $$f(x)$$ $$=log$$ $$sin$$$$-1$$ $$x2+x+1log$$ (x2-x+1) is

Correct option is 4None of these

Questions

The domain of f(x) $= \frac{\log (\sin^{- 1} \sqrt{x^{2} + x + 1})}{\log (x^{2} - x + 1)}$ is

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(-1 , 1)

(-1 ,0) ∪ (0 , 1)

(-1 , 0) ∪{ 1}

None of these

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detailed solution

Correct option is D

Here , log ( x2-x+1) is defined , when x2-x+1>0 and x2-x+1≠0⇒x∈R and x≠0 ,1⇒x∈R-{ 0,1}Again ,log (sin -1x2+x+1) exists , when 0< x2+x+1≤1⇒x2+x≤0 ⇒ x ∈[-1 , 0] x ∈ [-1, 0]

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The domain of f(x) =log sin-1 x2+x+1log (x2-x+1) is

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The domain of f(x) $= \frac{\log (\sin^{- 1} \sqrt{x^{2} + x + 1})}{\log (x^{2} - x + 1)}$ is