Is f(x)δ(x) Equal to f(2)δ(x)?

[athrun200]

Homework Statement

Homework Equations

The Attempt at a Solution

Can I write, say, $f(x) \delta(x)=f(2)\delta(x)$?
Since $\delta(x)$ =0 for x$\neq$0

 

[hunt_mat]

I think you can say $f(x)\delta (x-2)=f(2)\delta (x)$

 

[athrun200]

I think you can say $f(x)\delta (x-2)=f(2)\delta (x)$

Then if x=2, left hand side will become infinity and the right hand side 0.
Is it Ok?

 

[athrun200]

So what's wrong with my post in #1?

 

[Dick]

So what's wrong with my post in #1?

The integral of $f(x) \delta(x)$ over x is f(0). The integral of $f(2) \delta(x)$ over x is f(2). So no, they aren't the same.