Find $g(1)$ where $g(x)$ is the inverse of $f(x)=\sin(x)-2x+1$

Question

I was given the function$f(x)=\sin(x)-2x+1$

I was requested to prove that it's decreasing, which I did through its derivative. Since it's decreasing, it's monotonous and therefore injective. Thus, it has an inverse. So I was asked to find $g(1)$, where $g(x)$ is the inverse of $f(x)$. I have failed to find this inverse and I'm out of resources here (I'm only in the first year of my mathematics studies, so I'm quite a beginner). Does anybody know how can this problem be solved?

Answer 1

Since $f(0)=1$ and since $g=f^{-1}$, $g(1)=0$.