Question

Diketahui f(x)=√x²+1 dan (fog)(x)=1/x-2√x²-4x+5 tentukan (fog)–1(x)

Answer 1

  f(x) = √(x²+1)
f⁻¹(x) = √(x²-1)

(fog)(x) = (√(x²-4x+5))/(x-2)
             = √((x²-4x+5)/(x²-4x+4))
             = √((1/(x-2))² + 1)

             (fog)(x) = f(g(x))
√((1/(x-2))² + 1) = √(g(x))²+1)
                  g(x) = 1/(x-2)
                 g⁻¹(x) = (1+2x)/x

(fog)⁻¹(x) = g⁻¹(f⁻¹(x))
               = (1+2.(f⁻¹(x)))/(f⁻¹(x))
               = 2 + 1/(f⁻¹(x))
               = 2 + 1/√(x²-1)