Question

Jika f x= -3x + 1 dan g(x) = 2x /x-1, maka ( g^-1of^-1) (x) =​

Answer 1

Verified answer

f(x) = -3x+1

g(x) = 2x/(x-1)

(g⁻¹of⁻¹)(x) = ​(fog)⁻¹(x)

(fog)(x) = -3(2x/(x-1))+1

            = -6x/(x-1)+1(x-1)/(x-1)

            = (-6x+x-1)/(x-1)

            = (-5x-1)/(x-1)

       y = (-5x-1)/(x-1)

  yx-y = -5x-1

yx+5x = y-1

x(y+5) = y-1

       x = (y-1)/(y+5)

(fog)⁻¹(x) = (x-1)/(x+5)

// cara cepat mencari invers pembagian //

 f(x) = (ax+b)/(cx+d)

f⁻¹(x) = (-dx+b)/(cx-a)

// sehingga //

 (fog)(x) = -5x-1/x-1

(fog)⁻¹(x) = -(-1)x-1/x-(-5)

              = x-1/x+5