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), where a > 0 and n is a positive integer, then f(f(x))= (i) x^3 (ii) x^2 (iii) x (iv) -x

Derivative of f(x)=x^n is nx^(n-1) for any positive integer n.

If (2+sqrt(3))^n=I+f, where I and n are positive integers and 0

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)]

If a polynomial function f(x) satisfies f(f(f(x))=8x+21 , where pa n dq are real numbers, then p+q is equal to _______

If a polynomial function f(x) satisfies f(f(f(x))=8x+21 , where pa n dq are real numbers, then p+q is equal to _______

If f(x)=lim_(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equal to : (a) f(x)f(y) (b) f(x)+f(y) (c) f(x)-f(y) (d) none of these

If n is a positive integer and r is a nonnegative integer, prove that the coefficients of x^r and x^(n-r) in the expansion of (1+x)^(n) are equal.

If f(x)=x^3+b x^2+c x+da n df(0),f(-1) are odd integers, prove that f(x)=0 cannot have all integral roots.

The function f(x)=(sec^(-1)x)/(sqrt(x)-[x]), where [x] denotes the greatest integer less than or equal to x , is defined for all x in R (b) R-{(-1,1)uu{n"|"n in Z}} R^+-(0,1) (d) R^+-{n|n in N}