Find all points of discontinuity of the given function fx 1

Find all points of discontinuity of the given function: f(x) = {1 - x id x

Solution

chance of discontinuity is at x=1 or x=3

for x=1
f(1-) = 1-x = 1-1 = 0
f(1+) = x+2 =1+2 = 3
since f(1-) not equal to f(1+) , it is discontinuous at x=1

for x=3
f(3-) = x+2 = 3+2 = 5
f(3+) = x^2 -4 =3^2 -4 = 9-4 = 5
f(3) = x^2 -4 =3^2 -4 = 9-4 = 5
since f(3-) = f(3+)= f(3), it is continuous at x=3

Point of discontinuity is:
x=1