# Thread: Can't seem to get this stupid continuity problem...

1. ## Can't seem to get this stupid continuity problem...

Hey,

Any help on this problem would be appreciated. For some reason I can't for the life of me solve any of these questions when an '=' sign is introduced:

f(x) = {8x + 4 x < or = 9
and f(x) = {-4x + c x > 9

The question is : Find the value of 'c' that makes the function continuous.

Again, any help appreciated,

Craig.

2. Originally Posted by cjh824
Hey,

Any help on this problem would be appreciated. For some reason I can't for the life of me solve any of these questions when an '=' sign is introduced:

f(x) = {8x + 4 x < or = 9
and f(x) = {-4x + c x > 9

The question is : Find the value of 'c' that makes the function continuous.

Again, any help appreciated,

Craig.
for the function to be continuous ...

$f(9)$ must be defined

$\displaystyle \lim_{x \to 9^-} f(x)$ must equal $\displaystyle \lim_{x \to 9^+} f(x)$

$\displaystyle \lim_{x \to 9} f(x)$ must equal $f(9)$