Home
Class 12
MATHS
Let f:[0,1]vec[0,1] be a continuous func...

Let `f:[0,1]vec[0,1]` be a continuous function. Then prove that `f(x)=x` for at least one `0lt=xlt=1.`

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

Let f:[0,1] rarr [0,1] be a continuous function. Then prove that f(x)=x for at least one 0lt=xlt=1.

Let f: Rto(0,1) be a continuous function. Then, which of the following function (s) has (have) the value zero at some point in the interval (0,1)?

let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in[0,a] then int_0^a dx/(1+e^f(x) is equal to

Let f be a continuous function defined onto [0,1] with range [0,1]. Show that there is some c in [0,1] such that f(c)=1-c

Let f:Rto R be a twice continuously differentiable function such that f(0)=f(1)=f'(0)=0 . Then

Let f be continuous on the interval [0,1] to R such that f(0)=f(1)dot Prove that there exists a point c in [0,1/2] such that f(c)=f(c+1/2)dot

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1) =1 , then

Let f(x) be a continuous function in [-1, 1] and satisfies f(2x^2 - 1) = 2xf AA x in [-1, 1] . Prove that f(x) is identically zero for all x in [-1, 1]

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

Discuss the continuity of the function f defined by f(x)= (1)/(x), x ne 0 .

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Let f:[0,1]vec[0,1] be a continuous function. Then prove that f(x)=x f...

    Text Solution

    |

  2. Find x where f(x) = max {sqrt(x(2-x)),2-x} is non-differentiable.

    Text Solution

    |

  3. Discuss the differentiability of function f(x)=x-|x-x^2|

    Text Solution

    |

  4. Discuss the differentiability of f(x)="sin"|x|

    Text Solution

    |

  5. Discuss the continuity and differentiablity of f(x)=|x+1|+|x|+|x-1|...

    Text Solution

    |

  6. Discuss the differentiability of f(x)="max"{tan^(-1)x ,cot^(-1)x}dot

    Text Solution

    |

  7. find the values of a and b , such that f(x) ={ax^2+1,xle1 and x^2+ax...

    Text Solution

    |

  8. Discuss the differentiability of f(x)=|x[x]| ,-1 < x <= 2

    Text Solution

    |

  9. find the values of a and b , such that f(x) ={ax^2+1,xle1 and x^2+ax...

    Text Solution

    |

  10. Discuss the differentiability of f(x)=cos^(-1)((1-x^2)/(1+x^2))

    Text Solution

    |

  11. Which of the following function is non-differentiable in domain? (a)f(...

    Text Solution

    |

  12. Discuss the continuity of f(x)={1/(e^(x-1)),x!=1; 0,x=1

    Text Solution

    |

  13. Which of the following functions is not continuous AAx in R ?

    Text Solution

    |

  14. Find the value of f(0) so that the function. f(x)=(sqrt(1+x)-1+x^3)/x ...

    Text Solution

    |

  15. If the function f(x)={((x^2-(A+2)x+A)/(x-2), "for" x ne 2),(2, "for"...

    Text Solution

    |

  16. If the function f: R- {0}-> R given by f(x)=1/x-2/(e^(2x)-1) is conti...

    Text Solution

    |

  17. L e t f(x)=(1-tanx)/(4x-pi),x!=pi/4,x in [0,pi/2], Iff(x)i s continuou...

    Text Solution

    |

  18. If f(x)=(tan(pi/4+(log)e x))^((log)x e) is to be made continuous at x=...

    Text Solution

    |

  19. f(x)={(2xtanx-pi/(cosx) ,, x!=pi/2),(k ,, x=pi/2):} i s \ c o n t i n ...

    Text Solution

    |

  20. Discuss the continuity of f(x) ={{:(((x^(2))/|x|,xne0),(0,x=0):}

    Text Solution

    |

  21. Let f(x)={(1+3x)^(1/x), x != 0e^3,x=0 Discuss the continuity of f(x) a...

    Text Solution

    |