# Continuity of functions

1. Jun 18, 2012

### XodoX

1. The problem statement, all variables and given/known data

Give values of x where f(x)= x-1 / x2+4x+3 is continuous

f(x)= x2-4 / x2+x-2 Where x has removable discontinuity

2. Relevant equations

3. The attempt at a solution

Continuous, jump, infinite, removable.

It's been so long that I do not remember. I tried to look it up, but can not make sense of it. Continuous was continuous at all points, If I remember correctly. So I would have to plug in 1 and the result has to be 1. And it's removable when the factors on the top and bottom cancel. So it would be "removable" at -2. Not sure how to test for discontinuity. I can't really plug in a bunch of values until I find a hole. I suppose it's discontinuous when the equation is 0 ? So it would be all x except 1.
Same goes for jump and infinite.. not sure how to do this using an equation.

2. Jun 18, 2012

### ElijahRockers

For both equations, the functions is discontinuous if the denominator is ever equal to zero.

Both of the denominators are quadratic expressions which yield two distinct, real roots. Those roots are the values where your functions are discontinuous.

A removable discontinuity can be thought of as a 'hole' in a graph. That is, a discontinuity which can be repaired by filling in a single point.