Fourier transform of delta composed to a function

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I need your help! I would like to calculate the Fourier transform (or the Laplace transform) of \begin{align*} \delta(f(t)) \end{align*} where I know the Fourier transform (or the Laplace transform) of $f$. The function $f$ is on $\mathbb{R}$. If you prefer, I'm looking for the Fourier transform of \begin{align*} \mathbf{1}(f(t)=0) \end{align*} Thanks to everybody, any suggestions are helpful