Question

Câu 1: Cho hàm số :y= f(x) =\(\left|3x-1\right|\)

Tìm x biết: f(x) = 0 ; f(x) =1 ; f(x)= \(\dfrac{1}{2}\); f(x) =\(-\dfrac{2010}{2011}\)

Ai bik giúp mk vs, mk cần gấp lắm mọi người ơi ^ - ^

Answer 1

Ta có:\(f\left(x\right)=0\Rightarrow|3x-1|=0\Rightarrow3x-1=0\)

\(3x=0+1=1\)

\(x=1:3=\dfrac{1}{3}\)

\(f\left(x\right)=1\Rightarrow|3x-1|=1\Rightarrow3x-1=\pm1\)

*Với \(3x-1=1\Rightarrow3x=1+1=2\)

\(x=2:3=\dfrac{2}{3}\)

*Với \(3x-1=-1\Rightarrow3x=-1+1=0\)

\(x=0:3=0\)

\(f\left(x\right)=\dfrac{1}{2}\Rightarrow|3x-1|=\dfrac{1}{2}\Rightarrow3x-1=\pm\dfrac{1}{2}\)

*Với \(3x-1=\dfrac{1}{2}\Rightarrow3x=\dfrac{1}{2}+1=\dfrac{3}{2}\)

\(x=\dfrac{3}{2}:3=\dfrac{3}{2}.\dfrac{1}{3}=\dfrac{1}{2}\)

*Với \(3x-1=-\dfrac{1}{2}\Rightarrow3x=-\dfrac{1}{2}+1=\dfrac{1}{2}\)

\(x=\dfrac{1}{2}:3=\dfrac{1}{2}.\dfrac{1}{3}=\dfrac{1}{6}\)

\(f\left(x\right)=-\dfrac{2010}{2011}\Rightarrow|3x-1|=-\dfrac{2010}{2011}\Rightarrow x\in\varnothing\)