The graph is this half of a parabola.



The inverse is its projection in the identity line whose equation is
y = x, the dotted line below





Change f(x) to y



Interchange x and y.  You can interchange them now or later. 
I prefer to do it now, but your teacher might prefer to wait
to interchange them.  It really doesn't make any difference.



Solve for y by first swapping left and right sides:



Get 0 on the right side by subtracting x from both sides:



Use the quadratic formula:















Since y > 1, we must choose the + sign and discard the negative sign.
Then we don't need to keep the y > 1 because the equation guarantees
that y will always be greater than 1.



Next we change y to f-1(x):



The graph of that is the green curve below, which is the projection 
of the original (red) graph into the identity line, whose equation is y = x.



Edwin