The inverse of the given function is required.
The correct option is B. [tex]f^{-1}(x)=\dfrac{1}{x-1}[/tex]
The function is
[tex]f(x)=\dfrac{x+1}{x}[/tex]
So,
[tex]y=\dfrac{x+1}{x}\\\Rightarrow y=\dfrac{x}{x}+\dfrac{1}{x}\\\Rightarrow y=1+\dfrac{1}{x}\\\Rightarrow y-1=\dfrac{1}{x}\\\Rightarrow x=\dfrac{1}{y-1}\\\Rightarrow f^{-1}(x)=\dfrac{1}{x-1}[/tex]
The correct option is B. [tex]f^{-1}(x)=\dfrac{1}{x-1}[/tex]
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