GAIC Math 2024 Problem 82

A monotonically increasing function $\mathrm{f}(\mathrm{x})$ defined on $R^{+}$ satisfies $\mathrm{f}\left(\mathrm{f}(\mathrm{x})+\frac{2}{\mathrm{x}}\right)=-1$ consistently holds within its domain, then $\mathrm{f}(1)=$_____.