`f(x)=x^2-2a x+a(a+1),f:[a ,oo)vec[a ,oo)dot` If one of the solution of the equation `f(x)=f^(-1)(x)i s 5049 ,` then the other may be (a)5051 (b) 5048 (c) 5052 (d) 5050

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

The function f(x)=cot^(-1)x+x increases in the interval (a) (1,\ oo) (b) (-1,\ oo) (c) (-oo,\ oo) (d) (0,\ oo)

If f(x)=x^(100)+x^(99)+...+x+1, then f^(prime)(1) is equal to a. 5050 b. 5049 c. 5051 d. 50051

The function f : (0, oo) rarr [0, oo), f(x) = (x)/(1+x) is

The interval of increase of the function f(x)=x-e^x+tan(2pi//7) is (a) (0,\ oo) (b) (-oo,\ 0) (c) (1,\ oo) (d) (-oo,\ 1)

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

If f:[1, oo) rarr [1, oo) is defined as f(x) = 3^(x(x-2)) then f^(-1)(x) is equal to

The domain of the function f(x)=1/(sqrt(|x|-x)) is: (A) (-oo,oo) (B) (0,oo (C) (-oo,""0) (D) (-oo,oo)"-"{0}

The function f(x) = "max"{(1-x), (1+x), 2}, x in (-oo, oo) is

If e^x+e^(f(x))=e , then the range of f(x) is (-oo,1] (b) (-oo,1) (1, oo) (d) [1,oo)