Question

Cho hàm số f(x)=-2x+1. Tìm giá trị của x để f(1-2x)=f(2-x)

 Giúp mk nhé mk sẽ tick 

 

Answer 1

Ta có: \(f\left(x\right)=-2x+1\)

\(\Rightarrow\hept{\begin{cases}f\left(1-2x\right)=-2\left(1-2x\right)+1=4x-1\\f\left(2-x\right)=-2\left(2-x\right)+1=2x-3\end{cases}}\)

Vì \(f\left(1-2x\right)=f\left(2-x\right)\Rightarrow f\left(1-2x\right)-f\left(2-x\right)=0\)

Để \(f\left(1-2x\right)-f\left(2-x\right)=0\Rightarrow4x-1-\left(2x-3\right)=0\)

\(\Rightarrow4x-1-2x+3=0\Rightarrow2x+2=0\Rightarrow2\left(x+1\right)=0\)

\(\Rightarrow x+1=\frac{0}{2}=0\Rightarrow x=0-1\Rightarrow x=-1\)