Linear transformations?

[philipc]

I'm kind of stuck with the xf(0), hope this is the right place for this question?

let L(f) = 2Df - xf(0)
is L a linear transformation on the space of differentiable functions?

thanks for your help
Philip

[chroot]

I'm guessing that x is just some constant, in which case xf(0) is also just some constant. If so, it doesn't affect the linearity of the entire function.

- Warren

[philipc]

Thanks, I didn't think of it like that,
Philip

[Hurkyl]

The other possibility is that it's supposed to be written as:

L(f)(x) = 2(Df)(x) - x f(0)

so the x is not a constant.

[Max0526]

But nevertheless it's still linear in f.
Max.