Question 762384
The graph of {{{f^(-1)(x)}}} is the same as the graph of {{{f(x)}}}, but exchanging the x- and y-axes. You could also say that one graph is the reflection of the other across the {{{y=x}}} diagonal line.
{{{graph(300,300,-1,9,-1,9,x^2,sqrt(x),x)}}}
Of course, the graph of {{{f^(-1)(x)=sqrt(x)}}}  is only for {{{x>=0}}}.
 
From {{{x^2=sqrt(x)}}}, squaring both sides we get
{{{x^4=x}}} for {{{x>=0}}}
(You do not get {{{x=x}}} in any way).
{{{x^4=x}}} --> {{{x^4-x=0}}} --> {{{(x^3-1)x=0}}}  
whose solutions are {{{x=0}}} and {{{x=1}}},
corresponding to the origin and point (1,1).