4. Let the function $f: \mathbf{R}_{+} \rightarrow \mathbf{R}_{+}$ satisfy:
(1) If $x \leqslant y$, then $f(x) \leqslant f(y)$;
(2) When $x>0$,
$$
\begin{array}{l}
f\left(x^{4}\right)+f\left(x^{2}\right)+f(x)+f(1) \\
=x^{4}+x^{2}+x+1 .
\end{array}
$$

Find the function $f$.