Answer :
Assuming it's [tex]g(x)=\dfrac{1}{x-2}[/tex]
[tex]y=\dfrac{1}{x-2}\\ x-2=\dfrac{1}{y}\\ x=\dfrac{1}{y}+2\\ g^{-1}(x)=\dfrac{1}{x}+2[/tex]
[tex]y=\dfrac{1}{x-2}\\ x-2=\dfrac{1}{y}\\ x=\dfrac{1}{y}+2\\ g^{-1}(x)=\dfrac{1}{x}+2[/tex]