If f"(x) > 0 and f(1) = 0 such that `g(x) = f(cot^2x + 2cotx + 2) where 0 < x < pi`, then g(x) decreasing in (a, b). where `a + b + pi/4`…

If f'(x)>0 and f(1)=0 such that g(x)=f(cot^(2)x+2cot x+2) where0

If f''(x) gt 0 AA x in R, f'(4) = 0 and g(x) = f ( cot^2 x - 2 cot x + 5) , 0 lt x lt (pi)/(2) , then

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

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...... .

A function f(x) is such that f(x+1)=sqrt(f(x)+2) , where x in I^+ uu {0} and f(0)=0 then f(x) is a/an

Let f :R to R be a continous and differentiable function such that f (x+y ) =f (x). F(y)AA x, y, f(x) ne 0 and f (0 )=1 and f '(0) =2. Let f (xy) =g (x). G (y) AA x, y and g'(1)=2.g (1) ne =0 The number of values of x, where f (x) g(x):