Can rational functions inside logarithms have removable discontinuities?

[Qube]

Homework Statement

f(x) = ln[(x-x^2)/x]

Is x = 0 a removable discontinuity?

Homework Equations

Removable discontinuities are points that can be filled in on a graph to make it continuous.

The Attempt at a Solution

Is it? I know that with rational functions, canceling out factors can result in removable discontinuities. For example, the function (x+2)/[(x+2)(x+3)] has a removable discontinuity at x = -2 since the factor (x+2) can be canceled out.

What about rational functions inside logarithms?

 

[Ray Vickson]

Homework Statement

f(x) = ln[(x-x^2)/x]

Is x = 0 a removable discontinuity?

Homework Equations

Removable discontinuities are points that can be filled in on a graph to make it continuous.

The Attempt at a Solution

Is it? I know that with rational functions, canceling out factors can result in removable discontinuities. For example, the function (x+2)/[(x+2)(x+3)] has a removable discontinuity at x = -2 since the factor (x+2) can be canceled out.

What about rational functions inside logarithms?

What do you think? If you think the answer is NO, why would you think that? Ditto if you think the answer is YES.

 

[Simon Bridge]

@Qube: you appear to have answered your own question without realizing it.
Probably you need to focus on what it means for a discontinuity to be "removeable".

Removable discontinuities are points that can be filled in on a graph to make it continuous.

... not quite right is it? If you plotted y=(x+2)/[(x+2)(x+3)] would there be a discontinuity on the graph?