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?

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- February 5th 2010, 03:34 PMphalangecontinuity 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? - February 5th 2010, 05:24 PMProve It
- February 5th 2010, 06:04 PMArchie Meade
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.