Let `f(x) = asin^n x + bcosec^n x, x in (0, pi), a, b in R^+, n in N`, then(A) `f(x)` attains a maximum value which is independent of `n, a and b`.

Let f :R to R be a function, such that |f(x)|le x ^(4n), n in N AA n in R then f (x) is:

Let f :R to R be a function, such that |f(x)|le x ^(4n), n in N AA n in R then f (x) is:

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

Let f(x) = (x - 1)^(4) (x - 2)^(n), n in N . Then f(x) has a)a maximum at x = 1 if n is odd. b)a maximum at x = 1 if n is even c)a minimum at x = 1 if n is even d)a minima at x = 2 if n is even

Let f(x)=sin x cos^(2)x,x in[0,pi] .Let m be the number of values of x at which f(x) is minimum and n be the number of values of x at which f(x) is maximum. Then the value of m+n will be

Let f : N to N : f(x) =2 x for all x in N Show that f is one -one and into.

Let f : N rarr N be defined as f(x) = 2x for all x in N , then f is

Let f : N to N : f(x) =2 x for all x in N Show that f is one -one and into.