Laplace Transform Relations

Question

Let $\tilde{f} := \int_{0}^{\infty} f\cdot e^{-sx}dx$ be the Laplace transform of $f$, where $s$ is a complex number.

Is there anyway we can write $\hat{f} := \int_{0}^{\infty} f\cdot e^{x-sx}dx$ in terms of $\tilde{f}$?

Answer 1

$\tilde {f} (s-1)=\int_0^{\infty} f(x)e^{x-sx} dx$.