If `f: NrarrN`,and `x_2> x_1=> f(x_2)>f(x_1)` for `x_1,x_2 in N` a n d`f(f(n))=3nAAn in N ,` then `f(2)`=_________`

If f: N to N, and x_(2) gt x_(1) implies f(x_(2)) gt f(x) AA x_(1), x_(2) in N and f(f(n))=3n AA n in N," then " f(2)= _______.

Let f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040. Then the value of n is________

If f((x+2y)/3)=(f(x)+2f(y))/3AAx ,y in Ra n df^(prime)(0)=1,f(0)=2, then find f(x)dot

IF f(x) = ( x+2)/(3x-1) , then f(f(x)) is

If f is a function satisfying f (x +y) = f(x) f(y) for all x, y in N such that f(1) = 3 and sum _(x=1)^nf(x)=120 , find the value of n.

If f(x) satisfies the relation f(x+y)=f(x)+f(y) for all x , y in Ra n df(1)=5,t h e n (a) f(x)i sa nod dfu n c t ion (b) f(x) is an even function (c) sum_(n=1)^mf(r)=5^(m+1)C_2 (d) sum_(n=1)^mf(r)=(5m(m+2))/3

A=[1t a n x-t a n x1]a n df(x) is defined as f(x)=d e tdot(A^T A^(-1)) en the value of (f(f(f(ff(x))))_ is (ngeq2) _________.

A=[1t a n x-t a n x1]a n df(x) is defined as f(x)=d e tdot(A^T A^(-1)) en the value of (f(f(f(ff(x))))_ is (ngeq2) _________.

If f(x+f(y))=f(x)+yAAx ,y in Ra n df(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dxdot