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The inverse of the function f(x)= x/x-2 is; f-¹(x) = 2x/(x-1)
Since the function can be rewritten as;
By making x the subject of the function;
By swapping x and y; we then have;
The inverse function is therefore; f-¹(x) = 2x/(x-1)
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Rewritten by : Barada
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]
