Let `f(x) = log (1-x) +sqrt(x^(2)-1). `Then dom (f )=?A. `(1,oo)`B. `( – InterviewSolution

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1.	Let `f(x) = log (1-x) +sqrt(x^(2)-1). `Then dom (f )=?A. `(1,oo)`B. `(-oo,-1]`C. `[-1,1]`D. `(0,1)`
Answer» Correct Answer - B let `f(x) =g(x) =h (x) " where " g(x) =" log " (1-x) "and " h(x) =sqrt(x^(2)-1)` g (x) is defined only when `1-x gt 0 rArr x lt 1` So, dom (g) `=(-oo,1)` h(x) is defined only when `x^(2) -1 ge 1 0 rArr 1 " or " x le -1` `:. " dom " (h)= (-oo ,-1] uu [1,oo)` `:. " dom (f ) = " dom " (f ) nn" dom " (h)= (-oo,1]`

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Let `f(x) = log (1-x) +sqrt(x^(2)-1). `Then dom (f )=?A. `(1,oo)`B. `(-oo,-1]`C. `[-1,1]`D. `(0,1)`
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