Question

At which values of x is the function f(x) = x^2+x-6 / x-2 continuous and discontinuous?

continuous at x = ___

discontinuous at x = ____

Answer 1

f(x)=(x^2+x-6)/(x-2)=(x-2)(x+3)/(x-2). The common factor x-2 can be removed for all values of x≠2. At x=2 there is a discontinuity. In the limit as x→2, f(x)=x+3=5. So f(x) is continuous when x≠2 and discontinuous at x=2.

Comments

Thanks Rod for the answer but is there any other way rather than using not equal to (≠) symbol?

Or if there is exact value to be used? Thanks

---

You can use <> instead of ≠, because <> means less than or greater than. For all values of x other than x=2 the function is continuous because the denominator is zero only for x=2, and 0/0 can't be defined. If the function were to be plotted it would be the straight line y=x+3, with a "hole" at x=2. The hole would be located at (2,5).