Home
Class 12
MATHS
If f(x) is monotonically increasing func...

If f(x) is monotonically increasing function for all `x in R,` such that `f''(x)gt0andf^(-1)(x)` exists, then prove that `(f^(-1)(x_(1))+f^(-1)(x_(2))+f^(-1)(x_(3)))/(3)lt((f^(-1)(x_(1)+x_(2)+x_3))/(3))`

Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise EXAMPLE|6 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 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

If f(x)=x+(1)/(x) , then prove that : {f(x)}^(3)=f(x^(3))+3*f((1)/(x))

Let f'(x)gt0andf''(x)gt0 where x_(1)ltx_(2). Then show f((x_(1)+x_(2))/(2))lt(f(x_(1))+(x_(2)))/(2).

Let f'(x)gt0andf''(x)lt0 where x_(1)ltx_(2). Then show f((x_(1)+x_(2))/(2))gt(f(x_(1))+f(x_(2)))/(2)

If f: R to [0,∞) be a function such that f(x -1) + f(x + 1) = sqrt3(f(x)) then prove that f(x + 12) = f(x) .

If f(x),=x+(1)/(x), prove that [f(x)]^(3),=f(x^(3))+3f((1)/(x))dots

Let g(x)gt0andf'(x)lt0,AAx in R, then show g(f(x+1))ltg(f(x-1)) f(g(x+1))ltf(g(x-1))

Let (x) is a real function, defines as f(x) =(x-1)/(x+1), then prove that f(2x)=(3f(x)+1)/(f(x)+3).

If f:R->R is a function such that f(x)=x^3+x^2f''(2)+f'''(3) for all xepsilonR then prove that f(2)=f(1)-f(0)

If f(x)=((a^(2)-1)/(3))x^(3)+(a-1)x^(2)+2x+1 is monotonically increasing for every x in R then a can lie in

If f(x)=(1+x)(2+x^(2))^((1)/(2))(3+|x^(3)|)^((1)/(3)) then f'(-1) is

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If f(x) is monotonically increasing function for all x in R, such that...

    Text Solution

    |

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

    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) in R be given f(x)=overset(x)underset(1//x)int e^-(t+(1...

    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 rectagular sheet of fixed permeter with sides having thir lengths in...

    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+dand 0 ltb^(2)ltc, then in (-oo,oo)

    Text Solution

    |

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

    Text Solution

    |

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

    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)), u...

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

    Text Solution

    |