If `f(x) =(p-x^n)^(1/n)` ,`p >0` and` n` is a positive integer then `f[f(x)]` is equal to

If f(x) = (a-x^n)^(1/n), a > 0 and n in N , then prove that f(f(x)) = x for all x.

If f(x)=(a-x^(n))^(1//n),"where a "gt 0" and "n in N , then fof (x) is equal to

If (x-a)^(2m) (x-b)^(2n+1) , where m and n are positive integers and a > b , is the derivative of a function f then-

Evaluate int_(0)^(1)(tx+1-x)^(n)dx , where n is a positive integer and t is a parameter independent of x . Hence , show that ∫ 0 1 ​ x k (1−x) n−k dx= [ n C k ​ (n+1)] P ​ fork=0,1,......n, then P=

Let f(x)=x^(n) , n being a non-negative integer, The value of n for which the equality f'(x+y)=f'(x)+f'(y) is valid for all x,ygt0, is

If f(x)=x^2+x-42 and f(p-1)=0. what is a positive value of p ?

Let f(x)=x^n , n being a non negative integer. The value of n for which the equality f'(a+b)=f'(a)+f'(b) is valid for all a.bgt0 is

If f(x) = n , where n is an integer such that n le x lt n +1 , the range of f(x) is

Let x in(1,oo) and n be a positive integer greater than 1 . If f_n (x) =n/(1/log_2x+1/log_3x+...+1/log_nx) , then (n!)^(f_n (x)) equals to

Let f(x) be a real function not identically zero in Z, such that for all x,y in R f(x+y^(2n+1))=f(x)={f(y)^(2n+1)}, n in Z If f'(0) ge 0 , then f'(6) is equal to