The composed function is [tex]3x^7+3x [/tex]. We are going to express this function as [tex](f\circ g)(x)[/tex],
where neither of the functions are identity functions, that is f(x)≠x, and g(x)≠x.
Let [tex]g(x)=3x[/tex], and let [tex]\displaystyle{f(x)= (\frac{1}{3^6})x^7+x [/tex]
then
[tex]f(g(x))=\displaystyle{ (\frac{1}{3^6})(g(x))^7+g(x)=\displaystyle{ (\frac{1}{3^6})(3x)^7+3x[/tex]
[tex]=\displaystyle{ (\frac{1}{3^6})\cdot3^7x^7+3x=3x^7+3x[/tex]
Answer: [tex]g(x)=3x[/tex], [tex]\displaystyle{f(x)= (\frac{1}{3^6})x^7+x [/tex]
