If `alpha=e^(i2pi//7)a n df(x)=a_0+sum_(k-0)^(20)a_k x^k ,` then prove that the value of `f(x)+f(alpha, x)++f(alpha^6x)` is independent of `alphadot`

If alpha=e^(i2pi//7)a n df(x)=a_0+sum_(k=1)^(20)a_k x^k , then prove that the value of f(x)+f(alpha, x)++f(alpha^6x) is independent of alphadot

If alpha=e^(i2 pi/7) and f(x)=a_(0)+sum_(k-0)^(20)a_(k)x^(k) then prove that the value of f(x)+f(alpha,x)+...+f(alpha^(6)x) is independent of alpha.

If alpha=e^(2 pi(i)/(11)) and f(x)=5+sum_(k=1)^(60)A_(x)^(k), then the value of sum_(r=0)^(10)f(alpha^(r)x) is

If f(x)=sum_(k=0)^(n)a_(k)|x-1|^(k), where a_(i)in R, then

If a=(e^(2 pi i))/(7) and f(x)=A_(0)+sum_(k=1)^(20)A_(k)x^(k) then the value of sum_(r=0)^(6)f(a^(r)x)=n(A_(0)+A_(n)x^(n)+A_(2n)x^(2n)), then the value of n is

f(x) = (alpha x)/(x + 1) (x ne -1) , then for what value of alpha , f{f(x)} = x?

If f(x) = alpha x^n , prove that alpha= (f'(1))/n .