CyrieN181545 CyrieN181545
  • 25-10-2022
  • Mathematics
contestada

find the inverse function of g(x)= x-1÷x+5

Respuesta :

JuvenalW386044 JuvenalW386044
  • 25-10-2022
[tex]g(x)=\frac{x-1}{x+5}[/tex]

1. replace g(x) with y:

[tex]y=\frac{x-1}{x+5}[/tex]

2.Replace every x with a y and replace every y with an x

[tex]x=\frac{y-1}{y+5}[/tex]

3. Solve for y:

[tex]\begin{gathered} (y+5)x=y-1 \\ yx+5x=y-1 \\ yx-y=-1-5x \\ y(x-1)=-1-5x \\ y=\frac{-1-5x}{x-1} \end{gathered}[/tex]

4. Replace y with g−1(x) g− 1 ( x ):

[tex]g(x)^{-1}=\frac{-5x-1}{x-1}[/tex]

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