Let f:(1,3)→R be a function defined by f(x)=x[x]1+x2, where [x] denotes the greatest integer≤x . Then the range of f is:

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25,12∪35,45

25,45

25,35∪34,45

35,45

answer is A.

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Detailed Solution

f(x)=xx2+1;x∈(1,2) 2xx2+1;x∈[2,3) ∴f(x) is a decreasing function If x∈(1,2) then f(x)∈25,12 ff x∈[2,3) then f(x)∈35,45 ⇒ y∈25,12∪35,45

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