If fx=sinx+cosx,gx=x2-1, then gfx is invertible in the domain

fx=sinx+cosx,gx=x2-1⇒gfx=sinx+cosx2-1=sin2xClearly  gfx   is   invertible  in  -π2≤2x≤π2                        sinθ  is  invertible  when   -π/2≤θ≤π/2⇒     -π4≤x≤π4