Question

cho hàm số y=f(x)=|x-1|+2

a. Tính f(-2),f(1/2)

b. Tìm x sao cho f(x)= 3

Answer 1

a, \(f\left(-2\right)=\left|-2-1\right|+2=\left|-3\right|+2=3+2=5\)

\(f\left(\frac{1}{2}\right)=\left|\frac{1}{2}-1\right|+2=\left|-\frac{1}{2}\right|+2=\frac{1}{2}+2=2\frac{1}{2}\)

b, Để \(f\left(x\right)=3\) thì:

\(\left|x-1\right|+2=3\\ \Rightarrow\left|x-1\right|=1\\ \Rightarrow\left[{}\begin{matrix}x-1=1\\x-1=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\)

Vậy tại \(x\in\left\{0;2\right\}\) thì \(f\left(x\right)=3\)

Answer 2

Ta có: \(f\left(x\right)=\left|x-1\right|+2\)

a) Thay \(x=-2\) vào \(f\left(x\right)\) ta được:

\(f\left(-2\right)=\left|\left(-2\right)-1\right|+2\)

\(f\left(-2\right)=3+2\)

\(f\left(-2\right)=5.\)

+ Thay \(x=\frac{1}{2}\) vào \(f\left(x\right)\) ta được:

\(f\left(x\right)=\left|\frac{1}{2}-1\right|+2\)

\(f\left(x\right)=\frac{1}{2}+2\)

\(f\left(x\right)=\frac{5}{2}.\)

b) Để \(f\left(x\right)=3.\)

\(\Rightarrow\left|x-1\right|+2=3\)

\(\Rightarrow\left|x-1\right|=3-2\)

\(\Rightarrow\left|x-1\right|=1\)

\(\Rightarrow\left[{}\begin{matrix}x-1=1\\x-1=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1+1\\x=\left(-1\right)+1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\)

Vậy \(x\in\left\{2;0\right\}\) thì \(f\left(x\right)=3.\)

Chúc bạn học tốt!