Home
Class 11
MATHS
Let f(x) be defined on [-2,2] and be giv...

Let `f(x)` be defined on `[-2,2]` and be given by
`f(x)={(-1",",-2 le x le 0),(x-1",",1 lt x le 2):} and g(x)=f(|x|) +|f(x)|`.
Then find `g(x)`.

A

`{{:(,-x,-2 le x lt 0),(,0,0 le x lt 1),(,x-1,1 le x le 2):}`

B

`{{:(,-x,-2le x lt 0),(,0,0le x lt 1),(,2(x-1),1le x le 2):}`

C

`{{:(,-x,-2le x lt0),(,x-1,0 le x le 2):}`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|10 Videos

  • DISCRETE PROBABILITY DISTRIBUTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|40 Videos

  • HYPERBOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x le 0),(x-1",",0 lt x le 2):} and g(x)=f(|x|) +|f(x)| . Then find g(x) .

Let f(x)={{:(1+x",", 0 le x le 2),(3-x"," ,2 lt x le 3):} find (fof) (x).

Let f(x) be defined on [-2,2] and be given by f(x) = {−1;−2≤x≤0} and f(x) = {x−1 ; 0 < x ≤ 2 } ​ . and g(x)= f(|x|)+|f(x)| Find g(x)

f(x)={{:(x-1",", -1 le xle 0),(x^(2)",",0 lt x le 1):} and g(x)=sinx. Find h(x)=f(abs(g(x)))+abs(f(g(x))).

If f(x)={:{(3x^2+12x-1"," -1le x le2),(37-x ","2 lt x le 3):} then

If f(x)={{:(,x^(2)+1,0 le x lt 1),(,-3x+5, 1 le x le 2):}

Let f (x)= {{:(2-x"," , -3 le x le 0),( x-2"," , 0 lt x lt 4):} Then f ^(-1) (x) is discontinous at x=

Let a function f(x) defined on [3,6] be given by f(x)={{:(,log_(e)[x],3 le x lt5),(,|log_(e)x|,5 le x lt 6):} then f(x) is

Let f(x) ={:{(x, "for", 0 le x lt1),( 3-x,"for", 1 le x le2):} Then f(x) is

Let f(x) and g(x) be two functions given by f(x)=-1|x-1|,-1 le x le 3 and g(x)=2-|x+1|,-2 le x le 2 Then,

OBJECTIVE RD SHARMA ENGLISH-FUNCTIONS-Exercise
  1. If f(x) = (a-x^n)^(1/n) then fof(x) is (A) x (B) a-x (C) x^2 (D)...

    Text Solution

    |

  2. Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x l...

    Text Solution

    |

  3. Which of the following function from Z to itself are bijections? f(x)=...

    Text Solution

    |

  4. Which of the following functions from A={x in R :-1lt=xlt=1} to it...

    Text Solution

    |

  5. If f:RtoR is a function defined by f(x)=x^(3)+5 then f^(-1)(x) is

    Text Solution

    |

  6. Let f : A to B and g : B to C be the bijective functions. Then (g of ...

    Text Solution

    |

  7. Let f : R rarr R, g : R rarr R be two functions given by f(x) = 2x - 3...

    Text Solution

    |

  8. Let f:R to R be a function defined b f(x)=cos(5x+2). Then,f is

    Text Solution

    |

  9. Let f:N->N be defined by f(x)=x^2+x+1,x in N. Then f(x) is

    Text Solution

    |

  10. Let A={-1 le x le 1} and f:A to A such that f(x)=x|x| then f is:

    Text Solution

    |

  11. Let f: R-{3/5}->R be defined by f(x)=(3x+2)/(5x-3) . Then (a).f^-1(x)...

    Text Solution

    |

  12. If f(x)=2^(x),"then"f(0),f(1),f(2)..."are in"

    Text Solution

    |

  13. If the function f: RvecA given by f(x)=(x^2)/(x^2+1) is surjection, th...

    Text Solution

    |

  14. Which of the following functions is the inverse of itself? (a) f(x)=(1...

    Text Solution

    |

  15. If f(x) =(x-1)/(x+1)," then f(2x) is:"

    Text Solution

    |

  16. If f(x)=log((1+x)/(1-x))a n dg(x)=((3x+x^3)/(1+3x^2)) , then f(g(x)) i...

    Text Solution

    |

  17. If f(x)=a^x, which of the following equalities do not hold ? (i) f(...

    Text Solution

    |

  18. The interval in which the function y = f(x) = (x-1)/(x^2-3x+3) transfo...

    Text Solution

    |

  19. If f(x)=ax+b and g(x)=cx+d, then f(g(x))=g(f(x)) is equivalent to ...

    Text Solution

    |

  20. If f(x)=ax+b and g(x)=cx+d, then f(g(x))=g(f(x)) is equivalent to ...

    Text Solution

    |