KVPY SX SB Exam 05-Nov-2017 Question Paper

Let R be the set of real numbers and f : R→R be given by $\mathrm{f}\left(\mathit{x}\right)=\surd |\mathit{x}|-\log \left(1+|\mathit{x}|\right)$ . We now make the following assertions:
I. There exists a real number A such that f(x) ≤ A for all x.
II. There exists a real number B such that f(x) ≥ B for all x.