Answer:
The function is given below as
[tex]f(x)=\frac{x+1}{x}[/tex]
Concept:
we will substitute f(x)= y and make x the subject of the formula
[tex]\begin{gathered} f(x)=\frac{x+1}{x} \\ y=\frac{x+1}{x} \\ cross\text{ multiply, we will have} \\ xy=x+1 \\ xy-x=1 \\ x(y-1)=1 \\ divide\text{ both sides by y-1} \\ \frac{x(y-1)}{y-1}=\frac{1}{y-1} \\ x=\frac{1}{y-1} \\ replace\text{ y with x} \\ f^{-1}(x)=\frac{1}{x-1} \end{gathered}[/tex]
Hence,
The final answer is
[tex]\Rightarrow f^{-1}(x)=\frac{1}{x-1}[/tex]
OPTION B is the right answer
