We assume that the function is as follows:
[tex]f^{-1_{}}(2)=?[/tex]Then, we have that:
[tex]f^{-1}(x)=\frac{1}{f(x)}[/tex]Thus, if we have that:
[tex]f(2)=-2\Rightarrow f^{-1^{}_{}}(x)=\frac{1}{f(x)}\Rightarrow f^{-1}(2)=\frac{1}{f(2)}=\frac{1}{-2}\Rightarrow f^{-1}(2)=-\frac{1}{2}[/tex]Therefore, the value for the function is f^-1(2) = -1/2 or
[tex]f^{-1}(2)=-\frac{1}{2}[/tex]