Try PiecewiseExpand
:
PiecewiseExpand[
y == 33 x^(3/2) UnitStep[y - 1] + x^(-1)*5*E^x UnitStep[1 - y]]
You will get three candidate formulas for y
:
Plot[Tooltip@{(5 E^x)/x, (5 E^x)/x + 33 x^(3/2), 33 x^(3/2), 1}, {x,
0, 4}, PlotRange -> {0, 40}]
You may have to restrict the values of x
.