Find each xvalue at which f is discontinuous and for each xv

Find each x-value at which f is discontinuous and for each x-value, determine whether f is continuous from the right, or from the left, or neither.

f(x) =

Solution

f is discontinuous at 0 and 1

since x +4 is not equal to 4x^2 at 0

and x + 4 is not equal to 4 -x at 1

f is continuous from the left at 0

since limit exists and equal to f(0)

lim x-->0- (x+4) = 4 = f(0)

similarly for 1 form the right