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The domain of definition of the function $y = \frac{1}{\log_{10} (1 - x)} - \sqrt{x + 2} is$

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a

(−3,−2) excluding −2.5

b

[0,1] excluding 0.5

c

[−2,1) excluding 0

d

none of these

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detailed solution

Correct option is C

The given function is y=1log10⁡(1−x)-x+2 is For domain 1-x>0 and x is a non zero real number it implies x<1 and x is not equal to zero x+2≥0⇒x≥-2 hence, -2≤x<1 and x is not equal to zero Therefore, the domain of the given function is −2,1−0

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