The known function f (x) = x ^ 2 + C..] Let f (x) = x ^ 2 + C and f [f (x)] = f (x ^ 2 + 1), where C is a constant Let g (x) = f [f (x)] and find the analytic expression of G (x)

The known function f (x) = x ^ 2 + C..] Let f (x) = x ^ 2 + C and f [f (x)] = f (x ^ 2 + 1), where C is a constant Let g (x) = f [f (x)] and find the analytic expression of G (x)

f[f(x)]=[x^2+c]^2+c
f(x^2+1)=[x^2+1]^2+c
f[f(x)]=f(x^2+1),
So C = 1
g(x)=f[f(x)]=[x^2+c]^2+c=x^4+2x^2+2