Let f: [-1,3] arrow R be defined as f(x) = begincases |x|+[x] , &-1 le x

Question

Let f: [-1,3] arrow R be defined as f(x) = begincases |x|+[x] , &-1 le x < 1 x +|x | , 1 le x < 2 x+|x| ,& 2 le x le 3' endcases where [t] denotes the greatest integer less than or equal to t. Then, f is discontinuous at: (A) four or more points (B) only one point (C) only two points (D) only three points

Tardigrade Admin · Accepted Answer

f(x) = displaystyle begincases endcases beginmatrix-(x+1)&,&-1 le x<0 x&,&0 le x le1 2x&,&1 le x<2 x+2&,&2 le x<3 x+3&,&x=3 endmatrix function discontinuous at x = 0,1 ,3

Q. Let $f : [- 1, 3] \to R$ be defined as
$f (x) = ⎩ ⎨ ⎧ ∣ x ∣ + [x], x + ∣ x ∣, x + ∣ x ∣, - 1 \leq x < 1 1 \leq x < 2 2 \leq x \leq 3^{'}$
where [t] denotes the greatest integer less than or equal to t. Then, $f$ is discontinuous at:

four or more points

only one point

only two points

only three points

$f (x) = {$ $- (x + 1) x 2 x x + 2 x + 3,,,,, - 1 \leq x < 0 0 \leq x \leq 1 1 \leq x < 2 2 \leq x < 3 x = 3$
function discontinuous at $x = 0, 1, 3$

Q. Let f:[−1,3]→R be defined as f(x)=⎩⎨⎧​∣x∣+[x],x+∣x∣,x+∣x∣,​−1≤x<11≤x<22≤x≤3′​ where [t] denotes the greatest integer less than or equal to t. Then, f is discontinuous at: