Because lnX is increasing function (e x ≥ 0 can be proved to be derivative) and 0 < x < 1, lnx < ln 1 = 0,

Then xlnx < 0...( 1),

We also know that LNX-X+ 1 ≤ 0...(2)

Add (1) and (2).

You can get f(x) ≤0.