Consider the function `f:(-oo, oo) -> (-oo ,oo)` defined by `f(x) =(x^2 - ax + 1)/(x^2+ax+1) ;0 lt a lt 2`. which of the following is true ?

f:(-oo,oo)rarr(-oo,oo) defined by f(x)=|x| is

Consider the function f(-oo,oo)rarr(-oo,oo) defined by f(x)=(x^(2)-a)/(x^(2)+a), agt0 which of the following is not true?

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)

The function f : [0,oo)to[0,oo) defined by f(x)=(2x)/(1+2x) is

Consider the function f:(-oo,oo)to(-oo,oo) defined by f(x)=(x^2-a)/(x^2+a),a >0, which of the following is not true?(a) maximum value of f is not attained even though f is bounded. (b) f(x) is increasing on (0,oo) and has minimum at x=0 (c) f(x) is decreasing on (-oo,0) and has minimum at x=0. (d) f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.

Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x^2+a),a >0, which of the following is not true? maximum value of f is not attained even though f is bounded. f(x) is increasing on (0,oo) and has minimum at ,=0 f(x) is decreasing on (-oo,0) and has minimum at x=0. f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.