Find functions has a given propertiy

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Find a function $f:(0, \infty) \rightarrow(1, \infty)$ (not necessary continuos) satisfying that for each sequence $\left\{\mathrm{t}_{n}\right\} \subset(0, \infty), \lim _{n \rightarrow \infty} f\left(\mathrm{t}_{n}\right)=1$ if and only if $\lim _{n \rightarrow \infty} t_{n}=0^{+}$. " I know that exponential has this property but i want another examples "