We use the standard method of finding inverses. Note that, so that we have a unique inverse, we should assume that y is greater than or equal to 0. In order for 3x - 1 >= 0, x >= 1/3
Then, y = sqrt(3x - 1);
squaring both sides, y^2 = 3x - 1
3x = y^2 + 1
x = (y^2 + 1)/3
we then switch x and y in order to define this as an inverse.
f-1(x) = (x^2 + 1)/3 x >= 0