1. If the graph of the function $f(x)$ can be obtained by rotating the graph of the function $y=\lg (x+1)$ counterclockwise around the origin $O$ by $\frac{\pi}{2}$, then $f(x)=$
A. $10^{-x}-1$
B. $10^{x}-1$
C. $1-10^{-x}$
D. $1-10^{x}$
1. $\mathrm{A}$

Let $(x, y)$ be any point on the graph of $f(x)$. Then $(x, y)$, after a clockwise rotation of $\frac{\pi}{2}$ around point $O$, becomes $(y, -x)$, which lies on the graph of $y=\lg (x+1)$. Therefore, $-x=\lg (y+1)$, and $y=10^{-x}-1$.