Question

The greatest and the least value of the function $f\left(x\right)=\sqrt{1-2x+x^2}-\sqrt{1+2x+x^2,}x\in \left(-\infty .\infty \right)$ are

• A. $2,-2$
• B. $2,-1$
• C. $2,0$
• D. none

Answer 1

The correct option is A $2,-2$

R.E.F image

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

$\Rightarrow |1-x|-|1+x|$

As can be seen from

the graph,

max. value of $f\left(x\right)=2$

Min. value of $f\left(x\right)=-2$