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Question

# The domain of the function y=1{log10(3−x)}+√x+7

A
[-7, 3) - {2}
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B
[-7, 3] - {1}
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C
(-7, 3) - {0}
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D
(-7, 3)
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Solution

## The correct option is A [-7, 3) - {2}The function would be defined when the term 1{log10(3−x)} is real, which will occur when x < 3. However, if x = 2, then the denominator of the term becomes 0, which should not be allowed. The other limit of the function gets defined by the constraint defined by the term √x+7. For √x+7 to be real, x ≥ - 7 is the requirement. Hence, Required domain = - 7 ≤ x < 3, x ≠ 2 i.e., x ϵ [-7,3) - {2} Option (a) is correct.

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