Q1. How many roots does this equation possess?

3^|x|-|2-|x||=1

hi , rewrite the eq. as

    3^|x|-1 = |2-|x||

 or, we can write

      3^|x|-1 =  ||x|-2|

we will now do the graphical analysis of both the function  3^|x|-1   &  ||x|-2| .

if the graphs will intersect at apoint then at this point both the function will be equal

& this point will be the solu. of our eq.

we can  clearly say that there are only two solu. of the given eq.

 to draw the graph of first one,

1 . first we draw the 3^x . changing its -x axis by +xaxis we will get 3^{|x| . _{by pulling it downward  at a unit distance we will make graph of}} 3^{|x| _-1}

_{^{for second function,}}

  _{^{2.  draw the}} |x|  & pull it by 2 unit down ward . then we will invert that part of graph which is below x - axis  . this will be the graph of    ||x|-2|.