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The function f is continuous and has the...

The function `f` is continuous and has the property `f(f(x))=1-x` for all `x in [0,1]` and `J=int_0^1 f(x)dx`. Then which of the following is/are true? (A) `f(1/4)+f(3/4)=1` (B) the value of `J` equals to `1/2` (C) `f(1/3).f(2/3)=1` (D) `int_0^(pi/2) (sinxdx)/(sinx+cosx)^3` has the same value as `J`

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