Which of the following functions defined from `(-oo,oo)` to `(-oo,oo)` is invertible ?

Which of the following functions is increasing in (0 , oo) ?

Consider the function f:(-oo,oo)rarr(-oo,oo) defined by f(x)=(x^2-ax+1)/(x^2+ax+1), 0ltalt2 , and let g(x)=int_0^(e^x) (f\'(t)dt)/(1+t^2) . Which of the following is true? (A) g\'(x) is positive on (-oo,0) and negative on (0,oo) (B) g\'(x) is negative on (-oo,0) and positive on (0,oo) (C) g\'(x) changes sign on both (-oo,0) and (0,oo) (D) g\'(x) does not change sign on (-oo,oo)

Consider the function f:(-oo,oo)rarr(-oo,oo) defined by f(x)=(x^2-ax+1)/(x^2+ax+1), 0ltalt2 , and let g(x)=int_0^(e^x) (f\'(t)dt)/(1+t^2) . Which of the following is true? (A) g\'(x) is positive on (-oo,0) and negative on (0,oo) (B) g\'(x) is negative on (-oo,0) and positive on (0,oo) (C) g\'(x) changes sign on both (-oo,0) and (0,oo) (D) g\'(x) does not change sign on (-oo,oo)

If the function f:[1, oo) rarr [ 1,oo) defined by f(x) = 2^(x(x -1)) is invertible, then find f^(-1) (x).

Let f be the function f(x)=cos x-(1-(x^(2))/(2))* Then f(x) is an increasing function in (0,oo)f(x) is a decreasing function in (-oo,oo)f(x) is an increasing function in (-oo,oo)f(x) is a decreasing function in (-oo,0)

If f(x) is a differentiable even function, defined on (-oo, oo) and f^(')(-3) = -4 then f^(')(3) =

If f(x) is odd differentiable function defined on (-oo,oo) , such that f'(3)=2 , then f'(-3) is :

The range of the function f(x)=|x-1| is A. (-oo,0) B. [0,oo) C. (0,oo) D. R

The range of the function f(x)=|x-1| is A. (-oo,0) B. [0,oo) C. (0,oo) D. R