Question

Jika f(x)= √2 dengan x≥0 dan g(x)=x/(x+1) dengan x≠-1, maka tentukan :
a. rumus fungsi invers (g o f)^-1(x)
b. nilai fungsi (g o f)^-1(1/2)

Answer 1

F(x)= √x --> f⁻¹(x) = x²
g(x)= x/(x+1) --> g⁻¹(x) = x/ (x-1)

(gof)⁻¹(x)= f⁻¹ o g⁻¹ (x) = f⁻¹ { (x / (x-1) )}=  { x/(x-1)}² = x²/ (x-1)²

(gof)⁻¹( 1/2)=  (1/2)² / ( 1/2 - 1)² = (1/2)²/(-1/2)² = 1