Explain why f (x) = 1 / (x-3) ^3 is not continuous at x=3

a) f is not defined at x = - 3

b) f is not defined at x = 3

c) f is not defined at x = 0

d) f is not defined at x = 9

F (x) = 1 / (x-3) ^3

The denominator can't be equal to zero (we can't divide by zero), then:

(x-3) ^3 different 0

cubic root both sides:

cubic root [ (x-3) ^3 ] different cubic root (0)

x-3 different 0

Adding 3 both sides:

x-3+3 different 0+3

x different 3

Then the function f is not defined at x=3

Answer: Option b) f is not defined at x = 3