Let `f : [-1, 3] to R ` be defined as
`{{:(|x|+[x]", "-1 le x lt 1),(x+|x|", "1 le x lt 2),(x+[x]", "2 le x le 3","):}`
where, [t] denotes the greatest integer less than or equal to t. Then, f is discontinuous at

Options

A. four or more points
B. only two points
C. only three points
D. only one point

Answer

C

Explanation

Given function ` f : [-1, 3] to R ` is defined as
`f(x)={{:(|x|+[x]", "-1lexlt1),(x+|x|", "1 le xlt 2),(x+[x]", "2lexle3):}`
`{{:(-x-1", "-1lexlt0),(" x, "0lexlt1),(2x", "1lexlt2),(x+2", "2lexlt3),(" 6, "x=3):}`
`[:'" if "n le x lt n+1, AA n in "Integer," [x] = n]`
`:'" " underset( x to 0^(-)) lim f(x) =- 1 ne f(0)" "[:' f(0) = 0]`
`:'" " underset( x to 1^(-)) lim f(x) = 1 ne f(1)" "[:' f(1) = 2]`
`:'" " underset( x to 2^(-)) lim f(x) = 4= f(2)= underset( x to 2^(+)) lim f(x) = 4" "[:' f(2) = 4]`
and `underset( x to 3^(-)) lim f(x) = 5ne f(3)" " [:' f(3) = 6]`
`:.` Function f(x) is discontinuous at points 0, 1 and 3.