Question

Define f(x) so that ((x^3)-(x^2)-x-2)/((x^2)-4) is continuous at x = 2.

Answer 1

I know what it means for a function to be continuous at a certain point and I know that the above function is not continuous at x = 2. But I don't understand what the question means when it asks for one to define the function.

Answer 2

Hmmm i think they're asking you to do something like this.
we need to find a value for c that will make it a nice smooth curve

so whats happening is.. you have a HOLE at x=-2, and at x=2.
So we want to go in and patch the hole