Question

Xét sự biến thiên của hàm số f(x)=\(\dfrac{2x-1}{x+1}\) trên \(\left(-\infty;-1\right)\)

Answer 1

Ta co: \(f\left(x\right)=2-\dfrac{3}{x+1}\)

Suy ra

\(A=\dfrac{f\left(x2\right)-f\left(x1\right)}{x2-x1}=\dfrac{\dfrac{3}{x2+1}-\dfrac{3}{x1+1}}{x2-x1}=\dfrac{3\dfrac{x1-x2}{\left(x1+1\right)\left(x2+1\right)}}{x2-x1}\)

\(=-\dfrac{3}{\left(x1+1\right)\left(x2+1\right)}\)

Vi xet ham so tren \(\left(-\infty;-1\right)\)

Nen \(\left(x1+1\right)\left(x2+1\right)>0\)

\(\Rightarrow A< 0\) suy ra ham so nghich bien