Mathematics - Functions Question with Solution | TestHub

(i) $\mathrm{f}(\mathrm{x})=\tan \frac{\pi }{2}[\mathrm{x}]\mathrm{f}(\mathrm{x}+1)=\tan \frac{\pi }{2}[\mathrm{x}+1]=-\cot \frac{\pi }{2}[\mathrm{x}]$ $\begin{array}{rlr}& \mathrm{f}(\mathrm{x}+2)=\tan \frac{\pi }{2}[\mathrm{x}+2]=\tan \frac{\pi }{2}(2+[\mathrm{x}])& =\tan \left(\pi +\frac{\pi }{2}[\mathrm{x}]\right)=\tan \frac{\pi }{2}[\mathrm{x}]=\mathrm{f}(\mathrm{x})\end{array}$ $\therefore 2$ is period of f(x) 1 is not a period of f(x) $\therefore 2$ is the fundamental period