Say those two functions are #f(x)# and #g(x)#, and that them composed together would be #f(g(x))#.
We have that #f(g(x)) = 4/9 x#
So we could have #f(x) = 4x# and #g(x) = x/9#, so that:
#f(g(x)) = f(x/9) = 4(x/9) = 4/9 x#
Or it could also be that #f(x) = x/9# and #g(x) = 4x#. Due to multiplicative properties, we should get the same result:
#f(g(x)) = f(4x) = (4x)/9 = 4/9 x#
The functions could also be anything else where one must simplify as #4x# and the other as #x/9#. Here's an example:
#f(x) = (8x)/2# and #g(x) = x/sqrt(81)#
Or maybe even it is simply that the two functions should become #4/9 x# together, although it could be a bit risky:
#f(x) = x+3# and #g(x) = (4x - 27)/9#
#f(x) = sin^-1(x)# and #g(x) = sin((4x)/9)#
etc. The possibilities are endless.
