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.