Question 805922
<pre>f(x)= {{{1/(x+1)}}} and (f&#8728;g)(x)=x determine g(x)

Since (f&#8728;f<sup>-1</sup>)(x) = (f<sup>-1</sup>&#8728;f)(x) = x,

taking g(x) = f<sup>-1</sup>(x) will fill the bill of (f&#8728;g)(x)=x

So we find 

f<sup>-1</sup>(x)

Start with 

f(x) = {{{1/(x+1)}}}

Replace f(x) by y

y = {{{1/(x+1)}}}

Interchange x and y

x = {{{1/(y+1)}}}

Solve for y

Multiply both sides by (y+1)

x(y+1) = 1

xy + x = 1

Isolate the term in y

xy = 1 - x

Divide bith sides by x

y = {{{(1-x)/x}}}

Replace y by f<sup>-1</sup>(x)

f<sup>-1</sup>(x) = {{{(1-x)/x}}}

That will do for g(x), so 

g(x) = {{{(1-x)/x}}}

Edwin</pre>