Question 43: Given the function \(y=\frac{mx+2–2m}{x+m}\,\,\,\,\,(1)\) (m is a parameter). Find m so that the function (1) is covariable on each specified interval.

Condition \(x\ne -m\).

We have \(y′=\frac{m^2+2m–2}{(x+m)^2}\). For the given function to be covariant on each specified interval, then:

\(m^{2}+2 m-2>0 \Leftrightarrow\left[\begin{array}{l}m>-1+\sqrt{3}\\m<-1-\sqrt{3}\end{array}\right\)

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