# Given the one-to-one function r(x)=2/(x+5) Write the inverse function in inverse function notation.

Given the one-to-one function $r\left(x\right)=\frac{2}{x+5}$ Write the inverse function in inverse function notation.
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Dana Simmons
$r\left(x\right)=\frac{2}{x+5}\phantom{\rule{0ex}{0ex}}y=\frac{2}{x+5}\phantom{\rule{0ex}{0ex}}x+5=\frac{2}{y}\phantom{\rule{0ex}{0ex}}{r}^{-1}\left(x\right)=\frac{2}{x}-5\phantom{\rule{0ex}{0ex}}x\ne 0$
So $x\in \left(-\mathrm{\infty },0\right)\cup \left(0,\mathrm{\infty }\right)$