Can someone give me 3 rational functions that have removable discontinuities at x=2?

Question

Can someone give me 3 rational functions that have removable discontinuities at x=2?

Answer 1

f(x) = ( (x+3)(x-2) ) / (x-2)

f(x) = ( (x + 4)(x-2) ) / (x-2)

f(x) = ( x(x - 2) ) / (x - 2)

You can basically multiply any continuous function by (x - 2) / (x - 2) to get a removable discontinuity at x = 2.

Take care,

David

www.tutor-homework.com

Answer 2

Start with f(x) = (x-2) / (x-2).  Multiply the numerator by any polynomial you like.  Multiply the denominator by *almost* any polynomial you like--except, you just need to make sure that (x-2) appears as a factor upstairs at least as many times as it appears downstairs.

Now you can make as many examples as you want.

Answer 3

You have to redefine f(2) = lim f(x) as xtends to 2. Then a function discontinuous at x =2 becomes continuous. Read the meaning of removable discontinuity after this.