Home
Class 12
MATHS
Let {:f(x)= {(abs(x+1):,xlt1),(1-x:,x le...

Let `{:f(x)= {(abs(x+1):,xlt1),(1-x:,x le 1):}` and `{:f(x)= {(x-2:, xlt0),(x+3:, x ge0):}`. Then the function h - fg is given by :

A

`{:{(x^2+x+2:, xlt-1),(x^2-x-2:,-1le x lt 0),(x^2+ 4x+3:,0lexlt1),(-x^2 -2x +3:, xgt1):}`

B

`{:{(-x^2 + x +2 :,x lt-1),(x^2 - x -2 :,-1 le x lt0),(x^2-4x +3:,0 le xlt 1),(-x^2 - 2x + 3:,x ge1):}`

C

`{:{(-x^2+x+2:,xlt-1),(x^2-x-2:,-1 le xlt0),(x^2 + 4x +3 :, 0 le x le 1),(-x^2 - 2x +3:, x ge 1):}`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    MOTION|Exercise Exercise - 2 (Level-II)|6 Videos

  • FUNCTION

    MOTION|Exercise Exercise - 3|119 Videos

  • FUNCTION

    MOTION|Exercise Exercise - 1 ( JEE Main)|48 Videos

  • ELLIPSE

    MOTION|Exercise Exercise - 4 | Level-I Previous Year | JEE Main|20 Videos

  • HYPERBOLA

    MOTION|Exercise EXERCISE-4 (Level-II)|17 Videos

Similar Questions

Explore conceptually related problems

Let f(x){:{(1+sinx", "xlt0),(x^(2)-x+1ge0):} Then

If f(x)={(x-1",",xlt0),(1/4",",x=0),(x^2",",xgt0):} , then

Given f(x)={2x,xlt0, 0,xge0}"then "f(x) is

f(x)={(x+1,; xlt1), (2x-3,; xgeq1):}, evaluate lim_(x rarr 1)f(x).

MOTION-FUNCTION-Exercise - 2 (Level-I)
  1. If f : [0,oo)to [0,oo) and f(x) =(x)/(1+x), then f is

    Text Solution

    |

  2. Let f: (e, oo) -> R be defined by f(x) =ln(ln(In x)), then

    Text Solution

    |

  3. If f(x) = 2[x] + cosx, then f : R to R is (where [ * ] denotes great...

    Text Solution

    |

  4. If the real-valued function f(x) = px + sinx is a bijective function, ...

    Text Solution

    |

  5. Let S be the set of all triangles and R^+ be the set of positive real ...

    Text Solution

    |

  6. If g:[-2,2]vecR , where f(x)=x^3+tanx+[(x^2+1)/P] is an odd function, ...

    Text Solution

    |

  7. A function f(x)=(2x(sin x))/(2[(x+21 pi)/(pi)]-41)(1) Even function (...

    Text Solution

    |

  8. Let f(x)={:{(4, :, x lt-1),(-4x,:,-1 lex le 0):}. If f(x) is an even ...

    Text Solution

    |

  9. If the graph of the function f(x)=(a^(x)-1)/(x^(n)(a^(x)+1)) is symmet...

    Text Solution

    |

  10. If f(x)=sin(sqrt([a])x) (where [.] denotes the greatest integer functi...

    Text Solution

    |

  11. The fundamental period of function f(x) = [x] + [x + (1)/(3)] + [x + (...

    Text Solution

    |

  12. Let f: R to R be a periodic function such that f(T+x)=1" " where T...

    Text Solution

    |

  13. Fundamental period of the function f(x) = cos (sinx) + cos(cosx) is :

    Text Solution

    |

  14. If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) ...

    Text Solution

    |

  15. If 2f(xy) =(f(x))^(y) + (f(y))^(x) for all x, y in R and f(1) =3, then...

    Text Solution

    |

  16. No. of solution ge 7 for

    Text Solution

    |

  17. If the function f:[1,oo)to[1,oo) is defined by f(x)=2^(x(x-1)) then f^...

    Text Solution

    |

  18. Given below is graph of y = f(x) then

    Text Solution

    |

  19. Let f(x) = {{:(x + 1 , :, x £ 0) , (x , : , x gt 0):} and h (x) = |f(...

    Text Solution

    |

  20. Let {:f(x)= {(abs(x+1):,xlt1),(1-x:,x le 1):} and {:f(x)= {(x-2:, xlt0...

    Text Solution

    |