Question

Give a formula for the extended function that is continuous at the indicated point:

f(x) = ( x^2 - 9 ) / ( x + 3 ) , x = -3

Answer 1

To find the continuous extension of a discontinuous function, we try to remove the discontinuous factor. In this case:
f(x) = (x² - 9)/(x + 3)
= (x + 3)(x - 3)/(x + 3)
= (x - 3)
Value at x = -3:
-3 - 3 = -6