Function of a dirac delta

Question

I would like to know if it is possible to compute something like

$$\int_{-\infty}^{\infty}f\left(\delta(x-a)\right)dx,$$

where $f(x)$ is a function, or if it is even defined.

Thanks in advance!

Answer 1

Strictly, it's not defined, but there might be cases (other than $f$ being an affine function) where it can be given a meaning.

Answer 2

$$\int_{-\infty}^{\infty}f(x)(\delta(x-a))dx = f(a)$$ This comes from the fact that: $$\int_{-\infty}^{\infty}\delta(x)dx = 1$$