Let   f:-π3,2π3→0,4 be a function defined as fx=3sinx-cosx+2. Then f-1x is given by

y=fx=3sinx-cosx+2=2sinx-π6+2       ….   (1)Since f(x) is one-one and onto, f is invertible.From  1, sinx-π6=y-22or     x=sin-1y-22+π6or     f-1x=sin-1x-22+π6