Question:
If $f: R \rightarrow R$ is a function defined by $f(x)=[x-1] \cos \left(\frac{2 x-1}{2}\right) \pi$, where
[.] denotes the greatest
integer function, then $\boldsymbol{f}$ is :
Correct Option: , 4
Solution:
Doubtful points are $\mathrm{x}=\mathrm{n}, \mathrm{n} \in \mathrm{I}$
L.H.L $=\lim _{x \rightarrow n^{-}}[x-1] \cos \left(\frac{2 x-1}{2}\right) \pi=(n-2) \cos \left(\frac{2 n-1}{2}\right) \pi=0$
R.H.L $=\lim _{x \rightarrow n^{\prime}}[x-1] \cos \left(\frac{2 x-1}{2}\right) \pi=(n-1) \cos \left(\frac{2 n-1}{2}\right) \pi=0$
$f(n)=0$
Hence continuous.