Continuous function

[gerlansilva]

Determine the numbers where the function is continuous

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[Guest]

This is very odd! I would not expect you to be asked to do a problem connected with "continuous functions" if you do not know what "continuous function" means! I would think that if you did, you would have at least some work to show here.

A function, f, is continuous at x= a, if and only if
1) f(a) exits
2) [tex]\lim_{x\to a} f(x)[/tex] exists
3) [tex]\lim_{x\to a} f(x)= f(a)[/tex]
(Since, in order [tex]\lim_{x\to a} f(x)= f(a)[/tex] make sense, [tex]\lim_{x\to a} f(x)[/tex] and f(a) must exist we often just state (3).)

And in order that [tex]\lim_{x\to a} f(x)[/tex] exist the two "one sided limits" must exist and be equal.
It's easy to show that this is always true for polynomials so [tex]2x- 3[/tex] and [tex]x^2[/tex] are not a problem. The only possible problem is at x= 1, where the two polynomials meet. What is the value of f(1)? What is the limit, as x goes to 1, of [tex]2x- 3[/tex]? What is the limit, as x goes to 1, of [tex]x^2[/tex]?