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If f(x)=sin log((sqrt(4-x^(2)))/(1-x)), ...

If `f(x)=sin log((sqrt(4-x^(2)))/(1-x))`, then the domain of f(x) is ….

Text Solution

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The correct Answer is:
(-2, 1)
Given, `f(x)=sin log((sqrt(4-x^(2)))/(1-x))`
For domain, `(sqrt(4-x^(2)))/(1-x) gt 0,4-x^(2) gt 0 and 1-x ne 0`
`implies (1-x) gt 0 and 4-x^(2) gt 0`
`implies x lt 1 and |x| lt 2 implies -2 lt x lt 1`
Thus, domain `in (-2,1)`.
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