SOLUTION: Given h(x), find a pair of functions f and g such that h(x) = f<font face = "bookshelf symbol 7">g</font>g(x): h(x) = {{{sqrt( (7x^7+1)/(7x^7-1) ) }}}.

Given h(x), find a pair of functions f and g such that h(x) = fgg(x):
h(x) = square root . 

Pick g(x) as any expression in x from the whole expression



such that if you were to substitute u for that expression,
there will be no x's left.

-----------------
Suppose we pick u to be , then we replace both
the 's by u and get

  

g(x) is simply equal to what we picked u to be, that is,
g(x) =  

To get f(x) we substitute x for u in

 

and get 



So  

f(x) =  
g(x) =  

Checking:

h(x) = fgg(x) = f(g(x)) = f() =  .

Edwin