If `f(x) = sin(pi(x-[x])),AA x in (-(pi)/(2),(pi)/(2))`, where `[*]` denotes the greatest integer function, then

Options

A. 4
B. 5
C. 3
D. 2

Answer

C

Explanation

We have `f(x)=sin pi (x-[x])`
`Rightarrow f(x)={{:(,sin pi(x+2),"if "-2 le x lt -1),(,sin pi(x+1),"if "-1 le x lt 0),(,sin pi x,"if "0 le x lt 1),(,sin pi(x-1),"if "1 le x lt 2):}`
`Rightarrow f(x)={{:(,sin pi(x+2),"if "pi//2 lt x lt -1),(,sin pi(x+1),"if "-1 le x lt 0),(,sin pi x,"if "0 le x lt 1),(,sin pi(x-1),"if "1 le x lt pi//2):}`
`Rightarrow f(x)={{:(,sin pix,"if "-pi//2 lt x lt -1),(,-sin pi(x+1),"if "-1 le x lt 0),(,sin pi x,"if "0 le x lt 1),(,-sin pix,"if "1 le x lt pi//2):}`
The graph of f(x) is as shown in Fig.10

Clearly, f(x) is not intermediate at x=-1,0,1
Hence, there are three points of non-differenitable of f(x)