Question 32: Given the function (y=frac{mx+2m–3}{x–m}) (m is a parameter). Find all values of m such that the function is inverse on the interval ((2;+infty))

11/08/2021 // by admin// Leave a Comment

Question 32: Given the function \(y=\frac{mx+2m–3}{x–m}\) (m is a parameter). Find all values of m such that the function is inverse on the interval \((2;+\infty)\)

A. \(\left[\begin{array}{l}1

B. \(\left[\begin{array}{l}1-3\end{array}\right\)

C. Does not exist m

D. \(\left[\begin{array}{l}1

TXĐ: \(D=R \backslash\{m\}\)

We have: \(y^{\prime}=\frac{-m^{2}-2 m+3}{(xm)^{2}}\)

The above inverse function \((2;+\infty)\) IFF

\(\left\{\begin{array}{l} y^{\prime}<0 \\ m \notin(2 ;+\infty) \end{array} \Leftrightarrow\left\{\begin{array} {l} -m^{2}-2 m+3<0 \\ m \leq 2 \end{array} \Leftrightarrow\left\{\begin{array}{l} {\left[\begin{array}{l}m>1\\m<-3\end{array}{\Leftrightarrow}\left[\begin{array}{l}1

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« Question 31: Given the function (y=x^{3}+3 x^{2}-m x-4) . Find all values of parameter m so that the function is covariable on the interval ((-infty ; 0))

Question 33: Find all real values of parameter m so that the function (y=frac{x+2–2m}{x+m}) covariates on (–1;2). »

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