Question 1015265
<pre>
let {{{f(x)=1+1/x^2}}}, find a function {{{y=g(x)}}} so that {{{f(g(x)^"")=x}}}

Substitute y for x in the right side of f(x) and set it equal to x,
and solve for y:

{{{1+1/y^2}}}{{{""=""}}}{{{x}}}

{{{1/y^2}}}{{{""=""}}}{{{x-1}}}

Take reciprocals of both sides:

{{{y^2}}}{{{""=""}}}{{{1/(x-1)}}}

Take positive square roots of both sides:

{{{y}}}{{{""=""}}}{{{g(x)}}}{{{""=""}}}{{{1/sqrt(x-1)}}}

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Checking to see if {{{f(g(x)^"")=x}}}:

{{{f(g(x)^"")}}}{{{""=""}}}{{{f(1/sqrt(x-1))}}}{{{""=""}}}{{{1}}}{{{""+""}}}{{{matrix(2,1,"",(1[""])/((1/sqrt((x-1)))^2))}}}{{{""=""}}}

{{{1}}}{{{""+""}}}{{{matrix(2,1,"",(1[""])/((1/(x-1))))}}}{{{""=""}}}{{{1+(x-1)}}}{{{""=""}}}{{{1+x-1}}}{{{""=""}}}{{{x}}}

 Edwin</pre>