Number of solution of the equations: f(x-1) + f(x+1) = sin a, 0 < a , `pi/2`, where `f(x) = {:{(1-|x|, |x| le1),(0,|x|>1):}` is

Find the number of solution of the equations |cot x|= cot x +(1)/(sin x), when in [0,2pi]

The number of real solutions of the equations: tan^-1 sqrt(x(x+1)) + sin^-1 sqrt(x^2 + x+1) = pi/2 is

x_(1) and x_(2) are two solutions of the equation e^(x) cos x=1 , The minimum number of the solution of the equation e^(x) sin x =1 , lying between x_(1) and x_(2) can be

The number of real solution of the equation sqrt(1 + cos 2x) = sqrt2 sin^(-1) (sin x), -pi le x le pi , is

Find the number of real solution of the equation (cos x)^(5)+(sin x)^(3)=1 in the interval [0, 2pi]

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...... .

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……

Suppose f(x) is a function satisfying the folowing conditions: (i)f(0)=2,f(1)=1 (ii) f(x) has a minimum value at x=(5)/(2) (iii) for all xf'(x)= |{:(2ax,2ax-1,2ax+b+1),(b,b+1,-1),(2(ax+b),2ax+2b+1,2ax+b):}| The number of solutions of the equation f(x) +1=0 is

Consider two functions f(x)=1+e^(cot^(2)x) " and " g(x)=sqrt(2abs(sinx)-1)+(1-cos2x)/(1+sin^(4)x). bb"Statement I" The solutions of the equation f(x)=g(x) is given by x=(2n+1)pi/2, forall "n" in I. bb"Statement II" If f(x) ge k " and " g(x) le k (where k in R), then solutions of the equation f(x)=g(x) is the solution corresponding to the equation f(x)=k.

Find a quadratic function defined by the equation: f(x) = ax^2 + bx + c if f(0) = f(-1) = 0 and f(1)=2