Question 978200
{{{(2*f^(-1)-1)/(f^(-1)+2)=x}}}




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(wants more help)



That expression is essentially switching the places or roles of x and y.  You want a function that will give you x.


Try not using the "...to the negative one power" type notation.  You want a function g(x) so that f(x) and g(x) will undo each other.  That means that {{{g(f(x))=f(g(x))=x}}}.


You have your specific definition for f(x).  You want to use some other function g(x) AS INPUT to f(x) and the OUTPUT must be x.


{{{system(g(x)=YouNotYetKnow,f(x)=(2x-1)/(x+2),f(g(x))=x)}}}.


Form that last-specified composition:
{{{(2*g(x)-1)/(g(x)+2)=x}}}


Solve that equation for g(x).
The inverse of f(x) will be g(x).