InterviewSolution
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InterviewSolution
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The domain of definition of the function `f(x) = log_(3) {-log_(1//2)(1+(1)/(x^(1//5)))-1}`A. `(-oo, 1)`B. `(0, 1 )`C. `(1, oo)`D. none of these |
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Answer» Correct Answer - C Clearly, f(x) is defined if `- log_(1//2)(1+(1)/(x^(1//5)) - 1 gt 0, 1+(1)/(x^(1//5)) gt 0 and x ne 0` `log_(1//2) (1+(1)/(x^(1//5))) lt -1,1+x^(-1//5) gt 0 and x ne 0` `rArr 1+(1)/(x^(1//5)) gt ((1)/(2))^(-1),x^(-1//5) gt - and x in 0` `rArr (1)/(x^(1//5)) gt 1, (1)/(x^(1//5)) gt - and x ne 0` `rArr lt x lt 1,x gt - 1 and x ne 0 rArr 0 lt x lt1` |
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