If $f(x)=\sin \left[\pi^2\right] x-\sin \left[-\pi^2\right] x$, where $[x]=$ greatest integer $\leq x$, then which of the following is not true?

Let the functions " f " and " g " be $\mathrm{f}:\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R}$ given by $\mathrm{f}(\mathrm{x})=\sin \mathrm{x}$ and $\mathrm{g}:\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R}$ given by $g(x)=\cos x$, where $R$ is the set of real numbers

Consider the following statements:

Statement (I): $f$ and $g$ are one-one

Statement (II): $\mathrm{f}+\mathrm{g}$ is one-one

Which of the following is correct?

If $[x]^2-5[x]+6=0$, where $[x]$ denotes the greatest integer function, then

Let $f: R \rightarrow R$ be defined by $f(x)=x^2+1$. Then, the pre images of 17 and $-$3 , respectively are