1. The functions $y=f(x)$ and $y=g(x)$ have domains and ranges of $\mathbf{R}$, and both have inverse functions. Then the inverse function of
$$
y=f^{-1}\left(g^{-1}(f(x))\right)
$$

is $(\quad)$.
(A) $y=f\left(g\left(f^{-1}(x)\right)\right)$
(B) $y=f\left(g^{-1}\left(f^{-1}(x)\right)\right)$
(C) $y=f^{-1}(g(f(x)))$
(D) $y=f^{-1}\left(g^{-1}(f(x))\right)$
$-1 . \mathrm{C}$.
From $y=f^{-1}\left(g^{-1}(f(x))\right)$, we sequentially get
$$
\begin{array}{l}
f(y)=g^{-1}(f(x)), g(f(y))=f(x), \\
f^{-1}(g(f(y)))=x .
\end{array}
$$

Interchanging $x$ and $y$ yields $y=f^{-1}(g(f(x)))$.