Not quite,
The range is often more limited for the inverse.
Further constrainst on range often have to be introduced because the inverse must also be a function
Each x value must have AT MOST one y value.
eg
\(f(x)=sin x\) domain is all real x and range is [-1,1]
\(f^{-1}(x)=sin^{-1}x\) domain is [-1,1] but range must be limited. Uusally it is limited to \([-\pi/2,\pi/2]\)
.