Example 3. Write H a mapping from $(-\infty, \infty)$ to $(-3, 7)$.

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$(-\infty, \infty)$ to $(m, \infty)$ one-to-one mapping; from conclusion (three): $\mathrm{y}=\frac{10}{\mathrm{x}-\mathrm{m}+1}-3$ is a one-to-one mapping from $(\mathrm{m}, \infty)$ to $(-3,7)$; thus $y=$ $\left(10^{x}+\mathrm{m}\right)-\mathrm{m}+1-3$, i.e., $\mathrm{y}=\frac{10}{10^{x}+1}-3$ is a one-to-one mapping from $(-\infty, \infty)$ to $(-3,7)$.