Question 33: Find all real values of parameter m so that the function \(y=\frac{x+2–2m}{x+m}\) covariates on (–1;2).
Dk: \(x\ne -m\)
For the given function to be covariable on (–1;2), then y′>0 for all \(x \in(-1 ; 2)\)
\(\Leftrightarrow\left\{\begin{array}{l} m-(2-2 m)>0 \\ -m \notin(-1 ; 2) \end{array} \Leftrightarrow\left\{\ begin{array}{l} 3 m-2>0 \\ {\left[\begin{array}{l}m\geq1\\m\leq-2\end{array}\Leftrightarrow\left\{\left[\begin{array}{l}m>\frac{2}{3}\\m\geq1\end{array}\Leftrightarrowm\geq1\right\right\right}\\m\leq-2\end{array}\Leftrightarrowm\geq1\right\right\)
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