Let `f:[0, 1] rarr [0, 1]` be defined by `f(x) = (1-x)/(1+x), 0lexle1` & `g:[0,1]rarr[0,1]` be defined by `g(x)=4x(1-x), 0lexle1`
Determine the functions `fog` and `gof`.
Note that `[0,1]` stands for the set of all real members `x` that satisfy the condition `0lexle1`.

Explanation

`(fog)x=f{g(x)}=f{4x(1-x)}" "[because g(x)=4x(1-x)]`
`=(1-4x(1-x))/(1+4x(1-x))" "[becausef(x)=(1-x)/(1+x)]`
`=(1-4x+4x^(2))/(1+4x-4x^(2))=((2x-1)^(2))/(1+4x-4x^(2))`
and `(gof)x=g{f(x)}=g{(1-x)/(1+x)}" "[becausef(x)=(1-x)/(1+x)]`
`=4((1-x)/(1+x))(1-(1-x)/(1+x))=4((1-x)/(1+x))((2x)/(1+x))`
`=(8x(1-x))/((1+x)^(2))`