Home
Class 12
MATHS
Assume that inverse of the function f is...

Assume that inverse of the function f is denoted by g, then which of the
folllowing statement hold good?

A

If f is increasing, then g is also increasing

B

If f is decreasing, then g is increasing

C

The function g is injective

D

The function g is onto

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise EXAMPLE|23 Videos
  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|7 Videos
  • MATRICES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos
  • PAIR OF STRAIGHT LINES

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

Similar Questions

Explore conceptually related problems

The domain of the function f(x) is denoted by D_(f)

Which one of the following inequality holds good:

Given f(x)={3-[cot^(-1)((2x^3-3)/(x^2))] for x >0 and {x^2}cos(e^(1/x)) for x<0 (where {} and [] denotes the fractional part and the integral part functions respectively). Then which of the following statements do/does not hold good?

For alpha=pi/7 which of the following hold (s) good?

For a particle executing S.H.M. which of the following statements holds good :

If a,b,c,d,e are positive numbers, then which of the following holds good

Let f : R ->R defined by f(x) = min(|x|, 1-|x|) , then which of the following hold(s) good ?

For the following isomerisation reaction Cyclohexane hArr hexene -1, K = 1.732 Which of the following statements holds good at point 'A' ?

If a line has a vector equation, vecr=2hati +6hatj+lambda(hati-3hatj) then which of the following statements holds good ?

If f(x) = sin^(-1) x. cos^(-1) x. tan^(-1) x . cot^(-1) x. sec^(-1) x. cosec^(-1) x , then which of the following statement (s) hold(s) good?

ARIHANT MATHS ENGLISH-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Assume that inverse of the function f is denoted by g, then which of t...

    Text Solution

    |

  2. The least value of alpha in R for which 4ax^2+(1)/(x)ge1, for all xgt ...

    Text Solution

    |

  3. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

    Text Solution

    |

  4. Let f : R ->(0,oo) and g : R -> R be twice differentiable functions...

    Text Solution

    |

  5. Let f:(0,oo)vecR be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , then ...

    Text Solution

    |

  6. The fuction f(x)=2|x|+|x+2|-||x+2|-2|x|| has a local minimum or a loca...

    Text Solution

    |

  7. A rectangular sheet of fixed perimeter with sides having their lengths...

    Text Solution

    |

  8. A vertical line passing through the point (h, 0) intersects the ellips...

    Text Solution

    |

  9. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then

    Text Solution

    |

  14. If f(x)=x^2+2b x+2c^2 and g(x)= -x^2-2c x+b^2 are such that min f(x...

    Text Solution

    |

  15. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

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

    Text Solution

    |

  17. The maximum value of (cosalpha(1))(cos alpha(2))...(cosalpha(n)), un...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  21. about to only mathematics

    Text Solution

    |