Answer with Step-by-step explanation:
S={0,1,2,3,4,5,6,7,8,9}
A={0,2,4,6,8}
B={1,3,5,7,9}
C={0,1,2,3,4}
D={5,6,7,8,9}
a.A'=S-A
A'={0,1,2,3,4,5,6,7,8,9}-{0,2,4,6,8}
A'={1,3,5,7,9}
b.C'=S-C
C'={0,1,2,3,4,5,6,7,8,9}-{0,1,2,3,4}
C'={5,6,7,8,9}
c.D'=S-D
D'={0,1,2,3,4,5,6,7,8,9}-{5,6,7,8,9}
D'={0,1,2,3,4}
d.{0,2,4,6,8}
{1,3,5,7,9}
{0,1,2,3,4,5,6,7,8,9}=S
e.={0,2,4,6,8}
{0,1,2,3,4}
={0,1,2,3,4,6,8}
f.={0,2,4,6,8}
{5,6,7,8,9}
={0,2,4,5,6,7,8,9}
We know that a removable discontinuity occurs when:
The left and the right hand limit of the function exist at a point and are equal but is unequal to the function's value at that point.
Also it is a point on the graph such that it is undefined at that point.
The graph that has a removable discontinuity is attached to the answer.
Since, at x=0 the left hand and the right hand limit of the function exist but the function is not defined at x=0 , since in the graph there is a open circle at x=0 that means that the point is removed from the range.
