Home
Class 12
MATHS
Function f(x)=|x|-|x-1| is monotonically...

Function `f(x)=|x|-|x-1|` is monotonically increasing when `x<0` (b) `x >1` `x<1` (d) `0

A

`xlt0`

B

`xgt0`

C

`xlt0`

D

`0ltxlt1`

Text Solution

Verified by Experts

The correct Answer is:
4
f(X)=`|x|-|x-1|`
=`{{:(-x-(1-x),xlt0),(x-(1-x),0lexlt1),(x-(x-1),xlt0),(-1,xlt0),(2x-1,0lelt1),(1,xle1):}`

Graph of the function shows t hat f(X) clearly increases ion(0,1)
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|40 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|42 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.7|5 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|13 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Function f(x)=|x|-|x-1| is monotonically increasing when x 1 x<1 (d) 0

The function y=2x^2-ln|x| is monotonically increasing for values of x(!=0) satisfying the inequalities____ and monotonically decreasing for values of x satisfying the inequalities_____.

Let f(x) be and even function in R. If f(x) is monotonically increasing in [2, 6], then

Find the possible values of a such that f(x)=e^(2x)-(a+1)e^x+2x is monotonically increasing for x in Rdot

Let f(x)=|x^2-3x-4|,-1lt=xlt=4 Then f(x) is monotonically increasing in [-1,3/2] f(x) monotonically decreasing in (3/2,4) the maximum value of f(x)i s(25)/4 the minimum value of f(x) is 0

Prove that the function f(x)=(log)_e(x^2+1)-e^(-x)+1 is strictly increasing AAx in Rdot

f(x)=[x] is step-up function. Is it a monotonically increasing function for x in R ?

Find the complete set of values of alpha for which the function f(x) = {(x+1,xlt1 alpha , x =1 , is strictly increasing x=1 x^(2)-x+3,xgt1

The least integral value of x where f(x)=(log)_(1/2)(x^2-2x-3) is monotonically decreasing is________

f(x)=4tanx-tan^2x+tan^3x ,x!=npi+pi/2, (a)is monotonically increasing (b)is monotonically decreasing (c)has a point of maxima (d)has a point of minima

CENGAGE-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise (Single)
  1. The function x^x decreases in the interval (0,e) (b) (0,1) (0,1/e) ...

    Text Solution

    |

  2. Let f(x) =xsqrt(4ax-x^(2)),(agt0) Then f(x) is

    Text Solution

    |

  3. Function f(x)=|x|-|x-1| is monotonically increasing when x<0 (b) x >1...

    Text Solution

    |

  4. If f^(prime)(x)=|x|-{x}, where {x} denotes the fractional part of x , ...

    Text Solution

    |

  5. The length of the largest continuous interval in which the function f(...

    Text Solution

    |

  6. f(x)=(x-2)|x-3| is monotonically increasing in (-oo,5/2)uu(3,oo) (b)...

    Text Solution

    |

  7. f(x)=(x-8)^4(x-9)^5,0lt=xlt=10 , monotonically decreases in ((76)/(9,...

    Text Solution

    |

  8. For all x in (0,1) (a)e^x<1+x (b) (log)e (x+1) < x (c)sinx>x ...

    Text Solution

    |

  9. If f(x)=x e^(x(x-1)) , then f(x) is increasing on [-1/2,1] decreasing...

    Text Solution

    |

  10. If f(x)=k x^3-9x^2+9x+3 monotonically increasing in R , then k<3 (b) ...

    Text Solution

    |

  11. If the function f(x)=(Ksinx+2cosx)/(sinx+cosx) is strictly increasing ...

    Text Solution

    |

  12. Let f: RvecR be a function such that f(x)=a x+3sinx+4cosxdot Then f(x)...

    Text Solution

    |

  13. Which of the following statement is always true? (a)If f(x) is increas...

    Text Solution

    |

  14. Let f: RvecR be a differentiable function for all values of x and has ...

    Text Solution

    |

  15. Let f: Rvec be a differentiable function AAx in R . If the tangent dr...

    Text Solution

    |

  16. Let f(x) be a function such that f(x)=(log)(1/2)[(log)3(sinx+a]dot If...

    Text Solution

    |

  17. If f(x)=x^3+4x^2+lambdax+1 is a monotonically decreasing function of x...

    Text Solution

    |

  18. f(x)=|x loge x| monotonically decreases in (0,1/e) (b) (1/e ,1) (1,o...

    Text Solution

    |

  19. The set of value(s) of a for which the function f(x)=(a x^3)/3+(a+2)x^...

    Text Solution

    |

  20. The maximum value of the function f(x)=((1+x)^(0. 6))/(1+x^(0. 6)) in ...

    Text Solution

    |