Continuous and discontinuous functions

[Guest]

Find parameter b, such that the given function is discontinuous:
f(x)= [tex]\begin{cases} 2(x+2); x<1 \\ b; x=1\\ -4; x>1 \end{cases}[/tex]

[nathi123]

[tex]\lim_{x \to 1-0}f(x)= \lim_{x \to 1;x<1}f(x)=2.3=6[/tex];[tex]\lim_{x \to 1;x>1}f(x)=-4 ;x \in R;x>1 \Rightarrow \lim_{x \to 1;x<1}f(x) \ne \lim_{x \to 1;x>1}f(x)[/tex] for each b
[tex]\Rightarrow b \in R[/tex].

[Guest]

The limit, as x goes to 1 from below, is 6.
The limit, as x goes to 1 from above, is -4.

There is no value of b that will makes this function CONTINUOUS at x= 1!
Every values of b makes the function discontinuous at x= 1.