Home
Class 12
MATHS
Consider the function f:(-oo,oo)rarr(-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)`

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

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 ?

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

Let f:[4,oo)to[4,oo) be defined by f(x)=5^(x^((x-4))) .Then f^(-1)(x) is

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.

If f : [0, oo) rarr [0, oo) and f(x) = (x^(2))/(1+x^(4)) , then f is

If f :[2,oo)rarr(-oo,4], where f(x)=x(4-x) then find f^-1(x)

If f : [0, oo) rarr [2, oo) be defined by f(x) = x^(2) + 2, AA xx in R . Then find f^(-1) .

Let f:(-oo,2] to (-oo,4] be a function defined by f(x)=4x-x^(2) . Then, f^(-1)(x) is

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

Let f (x)= int _(x^(2))^(x ^(3))(dt)/(ln t) for x gt 1 and g (x) = int _(1) ^(x) (2t ^(2) -lnt ) f(t) dt(x gt 1), then: (a) g is increasing on (1,oo) (b) g is decreasing on (1,oo) (c) g is increasing on (1,2) and decreasing on (2,oo) (d) g is decreasing on (1,2) and increasing on (2,oo)