Question

find the x values of which f is not continuous: f(x): (x-3)/(x^2-9)

Answer 1

You cannot divide by zero. So x^2-9 cannot be zero.


If it were, then x^2-9 = 0 ---> x^2 = 9 ---> x = 3 or x = -3


This means that if either x = 3 or x = -3, then the denominator is zero.


So the function f is not continuous when x = 3 or x = -3

Answer 2

which of the discontinuities are removable?

Answer 3

since you can factor x^2-9 into (x+3)(x-3), the "x-3" terms will cancel out


So (x-3)/(x^2-9) simplifies to 1/(x+3)


So because the term "x-3" was removed, this means that the removable discontinuity is x = 3

Answer 4

thank you!