InterviewSolution
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InterviewSolution
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The domain of definition of the function `f(x) = sqrt(log_(x^(2)-1)) x` isA. `( sqrt2, oo)`B. `(0, oo)`C. `(1, oo)`D. none of these |
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Answer» Correct Answer - A We have, `f(x) = sqrt(log_((x^(2)-1))x)` Clearly,f(x) is define,if `log_((x^(2)-1)) x ge 0, x ge 0 ,x^(2)ge -1 ge 0 and x^(2) - 1 ne1` Now, `log_((x^(2)-1)) x gt 0` `rArr {{:(,x gt 1, "if" x^(2) - 1 gt 1),(,0 lt x lt 1, "if" x^(2) - 1 lt 1):}` `rArr {{:(,x ge1, "if" x^(2) - 2 lt 0 ),(,0 lt x lt 1,"if" x^(2)-2 lt 0 ):}` `rArr { {:(, x ge 1,"if" x lt - sqrt(2) or "," xgt sqrt(2)),(,0lt x lt 1 , "if"-sqrt(2) lt x ltsqrt(2)):}` `rArr x gt sqrt(2) or , 0 lt x lt 1` `rArr x in (0,1) uu (sqrt(2) , ooo)` And , `x gt 0, x^(2) -1 gt 0 and x^(2) - 1 ne 1` `rArr x in (1,sqrt(2))` From (i) and (ii), we get `x in (sqrt(2),oo)` Hence, domain of `f(x)` is `(sqrt(2),oo)` . |
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