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The domain of the function `f(x)=(sin^(-1)(3-x))/("In"(|x|-2))` isA. `[2,4]`B. `(2,3) cup (3,4)`C. `[2,oo)`D. `(-oo,-3) cup [2,oo)` |
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Answer» Correct Answer - B `f(x)=(sin^(-1)(3-x))/(log(|x|-2))` Let `g(x)=sin^(-1)(3-x)` or `-1 le 3 -x le 1` The domain of g(x) is [2, 4]. Let `h(x)=log(|x|-2)` I.e., `|x|-2 gt 0 " or " |x| gt 2` i.e., `x lt -2 " or " x gt 2` ` :. " Domain " (-oo, -2) cup (2 ,oo)` We know that `(f//g)(x)=(f(x))/(g(x)) AA x in D_(1) cap D_(2)-{x in R:g(x)=0}` Therefore, the domain of `f(x) " is " (2,4]-{3}=(2,3) cup (3,4].` |
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