Theproblem asks: For what values of constants a andb is the function f(x) continous on (-infinity, + infinity) ?
x + 2 , x < 1 f(x) = a , x = 1 bx^2 , x > 1
If you have time, please read below and confirm or correct mythinking on this problem:
To me the problem is saying:
That as the limit of x approaches 1 from the left(1-) and/or from the right (1+); f(x) =3.
So, for the limit to be continuous, f(x) = 3 it will haveto be true [when x is/close to 1]for each of the three (piecewiseequations? what is the correct terminology?).
So I think that means a = 3 and b = 3 when x = 1 or xapproaches 1. To check this mathematically, do I solve for eachvariable? I.e. 3 = bx^2 and 3 = a?
Am I understanding this problem correctly? If you havetime, please explain (in writing) what this problem means and howto solve it.
