Consider a polynomial (x) with real coefficients having the property (g(x)) = g((x)) for every polynomial g(x) with real coefficients. Determine and prove the nature

Consider a polynomial ƒ(x) with real coefficients having
the property ƒ(g(x)) = g(ƒ(x)) for every polynomial g(x)
with real coefficients. Determine and prove the nature of
ƒ(x).