Let f:-π3,2π3→0,4 be a function defined as fx=3sinx-cosx+2. Then f-1x is given by
sin-1x-22-π6
sin-1x-22+π6
2π3+cos-1x-22
none of these
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