Respuesta :

mberisso

Answer:

[tex]f^{-1}(x)=\frac{2x}{x-1}[/tex]

Step-by-step explanation:

Start by replacing f(x) by the variable "y" and solving for x in the equation:

[tex]f(x)=\frac{x}{x-2} \\y=\frac{x}{x-2}\\(x-2)\,y=x\\xy-2y=x\\xy-x=2y\\x(y-1)=2y\\x=\frac{2y}{y-1}[/tex]

Now do the final replacement using the inverse function notation, and replacing "y" with "x":

[tex]x=\frac{2y}{y-1} \\f^{-1}(x)=\frac{2x}{x-1}[/tex]

adioabiola

The inverse of the function f(x)= x/x-2 is; f-¹(x) = 2x/(x-1)

Since the function can be rewritten as;

  • y = x/x-2

By making x the subject of the function;

  • yx - 2y = x

  • x (y -1) = 2y

  • x = 2y/(y-1)

By swapping x and y; we then have;

  • y = 2x/(x-1)

The inverse function is therefore; f-¹(x) = 2x/(x-1)

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