If `f(x) = (h_1(x) - h_1(-x))(h_2(x)-h_2(-x))….(h_(2n+1)(x)-h_(2n+1)(-x))and f(200)=0`, then prove that f(x) is a many -one function.

If f(x) = log [(1+x)/(1-x)] , the prove that f[(2x)/(1+x^2)] =2f(x)

If f(x)=int((x^(2)+sin^(2)x))/(1+x^(2))sec^(2)xdx and f(0)=0 , then f(1)=

If f (x) = (x ^(5) - 1 ) (x ^(3) + 1), g (x) = (x ^(2) - 1 ) (x ^(2) - x + 1 ) and h (x) be such that f (x) = g (x) h (x), then lim _( x to 1) h (x) is

If f (x) = (x +2)/( 3x -1) , then f {f (x) } is

If (dx)/(x^(2)(x^(n)+1)^((n-1)//n))=-[f(x)]^(1//n)+c , then f(x) is

If f((x +1)/(2x-1)) = 2x, x in N , then the value of f(2) is equal to

If f(x)= |(1,1,1),(2x,x-1,x),(3x(x-1),(x-1)(x-2),x(x-1))| , then f(50)=

A function g(x) is defined as g(x) = (1)/(4) f(2x^(2) - 1) + (1)/(2) f(1- x^(2)) and f'(x) is an increasing function. Then g(x) is increasing in the interval