If `f:[1,oo)rarrR:f(x)` is monotonic and differentiable function and f(1)=1, then number of solutions of the equation `f(f(x))=(1)/(x^(2)-2x+2)` is/are……

Number of solution of the equations: f(x-1) + f(x+1) = sin a, 0 1):} is

If f is an even function, then find the realvalues of x satisfying the equation f(x)=f((x+1)/(x+2))

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

Let y=f(x) be a differentiable function such that f(−1)=2,f(2)=−1 and f(5)=3 If the equation f (x)=2f(x) has real root. Then find f(x)

Let F(x)=1+f(x)+(f(x))^2+(f(x))^3 where f(x) is an increasing differentiable function and F(x)=0 has a positive root, then

Let f:(0,oo)rarrR be a differentiable function such that f'(x)=2-(f(x))/(x) for all x in (0,oo) and f(1) ne 1. Then

Let f: (-1,1) rarr R be a differentiable function with f(0) = -1 and f'(0) = 1 let g(x) =[f(2f(x)+2)]^2 , then g'(0) =

Let f(x)be a monotic ploynomial of degree (2m-1) where m in N Then the equation f(x)-f(3x)+f(5x)+….+f((2m -1) has

Given a real valued fuction f(x) which is monotonic and differentiable , prove that for any real number a and b, int_(a)^(b){f^(2)(x)-f^(2)(a)} dx = int_(f(a))^(f(b))2x{b-f^(-1)(x)} dx