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Prove that the function f given by f(x)=...

Prove that the function `f` given by `f(x)=x-[x]` is increasing in `(0,\ 1)` .

Text Solution

Verified by Experts

We have given
`f(x)=x-[x]`
for `x in (0,1) implies [x]=0`
`f(x)=x`
`f′(x)=1`>`0`
Hence, `f(x)` is increasing for `x in (0,1)`.
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