Question

  Giúp mình (em) bài 1 với !!

Answer 1

a. ĐKXĐ: \(x\le1\)

b.

\(f\left(x\right)=\sqrt{1-x+2\sqrt{1-x}+1}=\sqrt{\left(\sqrt{1-x}+1\right)^2}=\sqrt{1-x}+1\)

Xét với \(x_1< x_2\le1\) ta có:

\(f\left(x_1\right)-f\left(x_2\right)=\sqrt{1-x_1}+1-\left(\sqrt{1-x_2}+1\right)=\sqrt{1-x_1}-\sqrt{1-x_2}\)

\(=\dfrac{1-x_1+\left(1-x_2\right)}{\sqrt{1-x_1}+\sqrt{1-x_2}}=\dfrac{x_2-x_1}{\sqrt{1-x_1}+\sqrt{1-x_2}}>0\) (do \(x_1< x_2\))

\(\Rightarrow f\left(x_1\right)>f\left(x_2\right)\Rightarrow\) hàm nghịch biến trên TXĐ