Hello, findmehere.genius!
I graphed the first one . . . Got the same answer as runninggag.
$\displaystyle \biggx22\bigg\:=\:x$ . Find value of $\displaystyle x.$ I'll graph it in baby steps . . .
We know what $\displaystyle y \:=\:x$ looks like: Code:

 *
 *
 *
     *     
* 
* 
* 

Then we have: .$\displaystyle y \:=\:x$
The absolute value says: anything below the xaxis is reflected upward. Code:

*  *
*  *
*  *
*  *
     *     


Then $\displaystyle y \:=\:x2$ moves the graph 2 units to the right. Code:
*  *
*  *
* *
 * *
   +  *     
 2

Then $\displaystyle y \:=\:x2 2$ moves the graph down 2 units. Code:

*  *
*  *
*  *
   *    *   
 * *
 *

Finally, $\displaystyle y \:=\:x2  2$
. . Anything below the $\displaystyle x$axis is reflected upward. Code:

*  *
*  * *
*  * * *
   *  +  *    
 2

There!
What does this graph have in common with $\displaystyle y = x$ ?
. . (See the first graph.)
We find that the graphs coincide for: .$\displaystyle 0 \:\leq\:x\:\leq\:2$