The domain of $$f(x)=x2+$$|$$x+3$$|$$+xx+2$$−$$1$$ is

Correct option is 3(−5,−2)∪(−1,∞)

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$The domain of f (x) = x^{2} + \sqrt{\frac{| x + 3 | + x}{x + 2} - 1} is$

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(−5,−3)∪(1,∞)

(−5,−2)∪(1,∞)

(−5,−2)∪(−1,∞)

R−{−2}

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detailed solution

Correct option is C

We must have |x+3|+xx+2≥1⇒ |x+3|−2x+2≥0 For |x+3|−2=0⇒x+3=±2⇒x=−5,−1 From the sign scheme we have x∈(−5,−2)∪(−1,∞) .

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The domain of f(x)=x2+|x+3|+xx+2−1 is

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$The domain of f (x) = x^{2} + \sqrt{\frac{| x + 3 | + x}{x + 2} - 1} is$