# A transform function from $(-\infty, \infty)$ to $(t_0, \infty)$?

I want to convert an integral from $(t_0, \infty)$ (or $(-\infty, t_0)$) range to $(-\infty, \infty)$ range by change of variable. What is the best transform function to do this - one that is simple, monotonic with $f(-\infty)=t_0$ and $f(\infty)=\infty$ (or $f(-\infty)=-\infty)$ and $f(\infty)=t_0$)?

I need this for an application of numerical quadrature with Gaussian weights.

Thanks.

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$f ( x ) = t_0 + e^x\$ is an example, or $g(x)=t_0 - e^{-x}$.
$$f(t)=t_0+\mathrm e^t$$