If `f(x) = (p - x^n)^(1/n), p gt 0` and n is positive integer, then the value of `f[f(x)]`

If f(x)=(a-x^n)^(1/n)," where "a gt0 and n is a positive integer, show that f[f(x)]=x.

If f(x)=(a-x^(n))^(1/n),agt0 and n is a positive integer, then prove that f(f(x)) = x.

If f(x)=x^n,n being a non-negative integer, then the values of n for which f'(alpha+beta)=f'(alpha)+f'(beta) for all alpha,beta>0 is

P(n):11^(n+2)+1^(2n+1) where n is a positive integer If P(n) = 14642, then the value of n is -

If f(x)={0 ,where x=n/(n+1),n=1,2,3.... and 1 else where then the value of int_0^2 f(x) dx is

P(n):11^(n+2)+1^(2n+1) where n is a positive integer p(n) is divisible by -

f(x)=e^(-1/x),w h e r ex >0, Let for each positive integer n ,P_n be the polynomial such that (d^nf(x))/(dx^n)=P_n(1/x)e^(-1/x) for all x > 0. Show that P_(n+1)(x)=x^2[P_n(x)-d/(dx)P_n(x)]

Prove that (""^n C_0)/x-(""^n C_1)/(x+1)+(""^n C_2)/(x+2)-.....+(-1)^n(""^n C_n)/(x+n)=(n !)/(x(x+1) . . . (x-n)), where n is any positive integer and x is not a negative integer.

Let f(n)=[1/2+n/100] , where [.] denotes the greatest integer function,then the value of sum_(n=1)^151 f(n)

Let f(x0 be a non-constant thrice differentiable function defined on (-oo,oo) such that f(x)=f(6-x)a n df^(prime)(0)=0=f^(prime)(x)^2=f(5)dot If n is the minimum number of roots of (f^(prime)(x)^2+f^(prime)(x)f^(x)=0 in the interval [0,6], then the value of n/2 is___