# Get Inverse Function in a certain domain

I'm trying to make Mathematica giving me the inverse function of $$f$$ (below) when restricted to the interval $$[v,1]$$.

Using ConditionalExpression or Piecewise as suggested in similar cases does not work.

Result should be the red curve in a way that I can apply the numerical derivative.

v=0.75; f[x_]:=v ArcSin[x]+Cos[ArcSin[x]]; F=InverseFunction[f]; Plot[{f[x],F[x]},{x,-1.3,1.3},AxesOrigin->{0,0}] 

• Desired picture can be obtained by ParametricPlot[{{x, f[x]}, {f[x], x}}, {x, -1.3, 1.3}], but this in not InverseFunction. – Alx Aug 26 '19 at 3:08
v=0.75; f[x_]:=v ArcSin[x]+Cos[ArcSin[x]]; F=InverseFunction[f]; ifun=Interpolation[Table[{f[x],x},{x,v,1,0.001}]]; inverse[y_]:=Piecewise[{{ifun[y],f[1]<y<f[v]},{Indeterminate,True}}] Plot[{f[x],F[x],inverse[x]},{x,-1.3,1.3},AxesOrigin->{0,0}]