# continuity of a function at x=4

• Feb 5th 2010, 03:34 PM
phalange
continuity of a function at x=4
given:

f(x)= ((x+2)/2), if x<4

f(x)= ((13-x)/3) if x>4

Is this function continuous at x=4? If not, is it removable discontinuity or non-removable discontinuity?
• Feb 5th 2010, 05:24 PM
Prove It
Quote:

Originally Posted by phalange
given:

f(x)= ((x+2)/2), if x<4

f(x)= ((13-x)/3) if x>4

Is this function continuous at x=4? If not, is it removable discontinuity or non-removable discontinuity?

Since the function is not defined for $x = 4$, how can it be continuous?
• Feb 5th 2010, 06:04 PM
Quote:

Originally Posted by phalange
given:

f(x)= ((x+2)/2), if x<4

f(x)= ((13-x)/3) if x>4

Is this function continuous at x=4? If not, is it removable discontinuity or non-removable discontinuity?

These are 2 linear functions,
one has a positive slope, the other negative.
f(4) = 3 in both cases, if 4 was allowed in the domain.

The "hole" at x=4 can be removed by filling it in,
therefore it is a removeable discontinuity.

The graph would then be continuous, albeit non-differentiable at x=4.