Home
Class 12
MATHS
If the function g:(-oo,oo)->(-pi/2,pi/2)...

If the function `g:(-oo,oo)->(-pi/2,pi/2)` is given by `g(u)=2tan^-1(e^u)-pi/2.` Then, `g` is

A

even and is strictly increasing in `(0,oo)`

B

odd and is strictly decreasing in `(-oo,oo)`

C

odd is strictly increasing in `(-oo,oo)`

D

neither even nor odd but is strictly increasing in `(-oo,oo)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|11 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

Let the function g: (-oo,oo)rarr (-pi //2,pi//2) be given by g(u) = 2 tan^(-1) (e^u)-pi/2 Then g is

If the function g:(-oo,oo)rarr(-(pi)/(2),(pi)/(2)) is given by g(u)=2tan^(-1)(e^(u))-(pi)/(2). Then g is

If g(x)=2tan^-1(e^x)-pi/2 is Even /odd

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)

f: (0,oo) to (-pi/2,pi/2)" be defined as, "f(x)=tan^(-1) (log_(e)x) . The above function can be classified as :

f:(-(pi)/(2),(pi)/(2))rarr(-oo,oo) defined by f(x)=tan x is

f(x)=tan x,x in(-(pi)/(2),(pi)/(2)) and g(x)=sqrt(1-x^(2)) then g(f(x)) is

If f:(-(pi)/(2),(pi)/(2))rarr(-oo,oo) is defined by f(x)=tan x then f^(-1)(2+sqrt(3))=

A function g(x) satisfies the following conditions (i) Domain of g is (-oo,oo) (ii) Range is g is [-1,7] (iii) g has a period pi and (iv) g(2)=3 Then which of the following may be possible.

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  2. e total number of local maxima and local minima of the function f(x) =...

    Text Solution

    |

  3. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

    Text Solution

    |

  4. The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt...

    Text Solution

    |

  5. If f(x)=x^(3)+bx^(2)+cx+dand 0 ltb^(2)ltc, then in (-oo,oo)

    Text Solution

    |

  6. If f(x)=x^(2)+2bx+2c^(2)and g(x)=-x^(2)-2cx+b^(2), such that minf(x)gt...

    Text Solution

    |

  7. The length of a longest interval in which the function 3sinx-4sin^(3...

    Text Solution

    |

  8. If f(x)=e^(1-x) then f(x) is

    Text Solution

    |

  9. The maximum value of (cosalpha(1))-(cos alpha(2))...(cosalpha(n)), u...

    Text Solution

    |

  10. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

    Text Solution

    |

  11. If f(x) is a cubic polynomil which as local maximum at x=-1 . If f(2)=...

    Text Solution

    |

  12. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  13. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  14. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  15. For the circle x^(2)+y^(2)=r^(2), find the value of r for which the ar...

    Text Solution

    |

  16. Find a point on the curve x^2 + 2y^2 = 6, whose distance from the li...

    Text Solution

    |

  17. Let f:R rArr R be defined as f(x)=|x|+|x^2-1| The total number of p...

    Text Solution

    |

  18. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

  19. Let f be a function defined on R (the set of all real numbers) such th...

    Text Solution

    |

  20. The maximum value of the expression (1)/(sin^(2)theta+3sinthetacosthet...

    Text Solution

    |