If `f(x)=x^(2)-2x+2,` `f: [1 rarr oo )` then the number of sloutions of the equation `f(x)=f^(-1)(x)` is?

Let f(x)=2x+1. AA x in R , then the solution of the equation f(x)=f^(-1)(x) is

Let F:[3,infty]to[1,infty] be defined by f(x)=pi^(x(x-3) , if f^(-1)(x) is inverse of f(x) then the number of solution of the equation f(x)=f^(-1)(x) are

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 f(x)=x^(2)-x+1, AA x ge (1)/(2) , then the solution of the equation f(x)=f^(-1)(x) is

Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 ,AA x in (0,oo) also f (0)=0, Again f'(x) lt 0 ,AA x in (-oo, -1) and f '(x) gt 0, AA x in (-1,oo) also f '(-1)=0 given lim _(x to -oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. If f'(x) lt 0 AA x in (0,oo)and f'(0)=1 then number of solutions of equation f (x)=x ^(2) is : (a) 1 (b) 2 (c) 3 (d) 4

Let f and g be two differentiable functins such that: f (x)=g '(1) sin x+ (g'' (2) -1) x g (x) = x^(2) -f'((pi)/(2)) x+ f'(-(pi)/(2)) The number of solution (s) of the equation f (x) = g (x) is/are :

If f(x) = x^2 - 3x + 4 , then find the values of x satisfying the equation f(x) = f(2x + 1) .

If f:[a,oo)->[a,oo) be a function defined by f(x)=x^2-2a x+a(a+1) . If one of the solution of the equation f(x)=f^(-1)x is 2012 , then the other may be

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

If f(x)=sqrt(x^(2)-2x+1), then f' (x) ?