1.6. 1* Let the function $f: D \rightarrow D$, for any $x \in D$, denote $f^{(0)}(x)-x, f^{(n+1)}(x)-$ $f\left(f^{(n)}(x)\right), n=0,1,2, \cdots$. The function $f^{(n)}(x)$ defined in this way is called the $n$-th iteration of $f(x)$.
Find the $n$-th iteration $f^{(n)}(x)$ for the following functions $f(x)$.
(1) $f(x)=x+c$, where $c$ is a constant;
(2) $f(x)=a x+b$, where $a, b$ are constants, and $a \neq 1$;
(3) $f(x)=\frac{x}{1+a x}$, where $a$ is a constant;
(4) $f(x)=x^{m}$, where $m$ is a given positive integer.
(1) $f^{(n)}(x)=x+n c$.

(2) $f^{(n)}(x)=a^{n} x+\left(1+a+\cdots+a^{n-1}\right) b=a^{n} x+\frac{1-a^{n}}{1-a} b$.

(3) $f^{(n)}(x)=\frac{x}{1+n a x}$.

(4) $f^{(n)}(x)=x^{m^{n}}$.