Question

Draw the graph of function $f:R\to R$ defined by $f\left(x\right)=\left|x-2\right|$ . Also write its domain and Range.

Answer 1

Given

$f\left(x\right)=|x-2|$

Case 1 ,if $x>2$

Then,

$f\left(x\right)>0$

$(x-2)>0$

$x>2$

Domain become all real number greater than 2

And range also become all real number greater than $2$

Case 2 if $x<2$

Then ,

$f\left(x\right)<0$

$-(x-2)<0$

$-x+2<0$

$-x<-2$

$x>2$

Domain become all real number greater than 2

And range also become all real number greater than 2