we have teh function
[tex]g(x)=\frac{1}{x}-2[/tex]step 1
Let
y=g(x)
[tex]y=\frac{1}{x}-2[/tex]step 2
Exchange the variables
x for y and y for x
[tex]x=\frac{1}{y}-2[/tex]step 3
Isolate the variable y
[tex]\begin{gathered} \frac{1}{y}=x+2 \\ y=\frac{1}{(x+2)} \end{gathered}[/tex]step 4
[tex]g^{(-1)}(x)=\frac{1}{x+2}[/tex]