Thread: Continuity of hybrid function - Trying to find the value of c

Did I do this correct?

determine the values of c such that the function f is continuous on the entire real line

f(x)={x+3 if x less than or equal to 2
cx+6 if x>2


lim x->2+ cx+6=2c+6

lim x->2- x+3=5

2c+6=5
-6 -6
2c/2=-1/2

c=-1/2

Originally Posted by LAPOSH42

Did I do this correct?

determine the values of c such that the function f is continuous on the entire real line

f(x)={x+3 if x less than or equal to 2
cx+6 if x>2


lim x->2+ cx+6=2c+6

lim x->2- x+3=5

2c+6=5
-6 -6
2c/2=-1/2

c=-1/2

That is correct.

Here is some simple LaTeX code
[TEX]\lim _{x \to 2^ + } f(x) = 2c + 6[/TEX] gives