Question

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

Answer 1

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