Mohon dibantu kak.soalnya mau dikumpulin besok!!! Pleaseee Invers dan komposisi fungsi

fungsi komposisi

dan Invers

*

f(x) = (2x – 1)/ (x + 1)

g(x) = 3x – 1

*

f(x)= (ax + b)/ (cx +d) –> f⁻¹(x) =  (dx – b)/(-cx +a)

*

gof(x)= g { f(x) } = g { (2x  -1) / (x + 1)}

gof(x) = 3(2x -1 ) / (x + 1)    - 1

gof(x) = (6x -3)/(x + 1) – (x – 1)/(x -1)

gof(x) = (6x -3 -x + 1) / (x- 1)

gof(x)= (5x – 2)/ (x-1)

*

fog (x)= f { g(x)} = f (3x – 1)

fog(x) =  { 2(3x – 1) – 1 } / { 3x -1 + 1}

fog(x)  = ( 6x – 2 – 1) / (3x)

fog(x) = (6x – 3) / (3x)  = 3(x – 1)/ 3(x)

fog(x) = (x – 1)/x

*

c) {f⁻¹ o g⁻¹) x = (gof)⁻¹(x)

(gof)(x) = (5x – 2)/ (x-1)

(gof)⁻¹(x) = (x + 2)/(-x + 5)

{f⁻¹ o g⁻¹}(x)  = (x + 2) /(-x +5)

*

e)  {g⁻¹ o f⁻¹)(x) = (fog)⁻¹ (x)

fog(x) = (x -1)/(x)

(fog)⁻¹(x)= (x + 1) /(-x)

{g⁻¹ o f⁻¹}(x) = (fog)⁻¹(x)= (x + 1)/ (-x) = – (x +1) /(x)

*

f)  {gof}⁻¹ (x) =

(gof)(x) = (5x – 2)/ (x-1)

(gof)⁻¹(x) = (x + 2)/(-x + 5)