Home
Class 12
MATHS
If g(x)=2-|x|,x epsilon[-1,3] and f(x)=-...

If `g(x)=2-|x|,x epsilon[-1,3]` and `f(x)=-1+|x-2|,0 le x le 4`
On the basis of above information answer the following questions:
Range of the function `y=g(f(x))` is

A

`[1,2]`

B

`[0,1]`

C

`[0,3]`

D

`[0,2]`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

f(x)=abs(x-1)+abs(x-2), -1 le x le 3 . Find the range of f(x).

Find the range of the function f(x)=cot^(-1)(log)_(0. 5)(x^4-2x^2+3)

Redefine the function f(x)= |x-2| + |2 + x|, -3 le x le 3

Let A = {-1,0,1,2}, B = {-4,-2,0,2} and f , g : A rarr B be functions defined f(x) = x^(2)-x, x inR and g(x) = 2 |x-(1)/2|-1,x inR . Are f and g equal ? Justify your answer. (Hint : One may note that two functions f : A rarr B and g : A rarr B such that f (a) = g(a) A a inA, are called equal functions).

"If "f(x)={{:(,-x-(pi)/(2),x le -(pi)/(2)),(,-cos x,-(pi)/(2) lt x le 0),(,x-1,0 lt x le 1),(,"In "x,x gt 1):} then which one of the following is not correct?(a)f(x) is continuous at x = - (pi)/(2) (b)f(x) is not differentiable at x = 0 (c)f(x) is differentiable x = 1 (d) none of them

f(x)= 3x^(2)-1 and g(x)= 3 + x . If f= g then the value of x is…….

Find the values of x for which the functions f(x)= 3x^(2)-1 and g(x)= 3 + x are equal

If f(x)={{:(,x[x], 0 le x lt 2),(,(x-1)[x], 2 le x lt 3):} where [.] denotes the greatest integer function, then (x) is continuous at x=2

If f and g are two real valued functions defined as f(x)= 2x+1 and g(x)= x^(2)+1 , then find (f)/(g) .

f(x)= (1)/((x-1) (x-2)) and g(x)= (1)/(x^(2)) . Find the points of discontinuity of the composite function f(g(x))?

ALLEN -TEST PAPERS-MATHEMATICS
  1. The equation x^(4)-2x^(3)-3x^(2)+4x-1=0 has four distinct real roots x...

    Text Solution

    |

  2. Which of the following is/are correct

    Text Solution

    |

  3. If g(x)=2-|x|,x epsilon[-1,3] and f(x)=-1+|x-2|,0 le x le 4 On the b...

    Text Solution

    |

  4. If g(x)=2-|x|,x epsilon[-1,3] and f(x)=-1+|x-2|,0 le x le 4 On the b...

    Text Solution

    |

  5. If x=sin alpha, y=sin(alpha+(4pi)/3),z=sin(alpha+(8pi)/3) u=cos alph...

    Text Solution

    |

  6. If x=sin alpha, y=sin(alpha+(4pi)/3),z=sin(alpha+(8pi)/3) u=cos alph...

    Text Solution

    |

  7. Consider the following species. ul(N)(SiH(3))(3),ul(N)(GeH(3))(3),ul...

    Text Solution

    |

  8. lim(xto oo) (sqrt(x^(2)-x+1)-(ax+b))=0 then for kge2, kepsilonN which...

    Text Solution

    |

  9. Suppose a and b are integers such that x^(2)+ax+b+1=0 has positive int...

    Text Solution

    |

  10. If f'(x^(2))=(ln x)/(x^(2)) and f(1)=-1/4 then which of the following ...

    Text Solution

    |

  11. If alpha=3sin^(-1)(2/3) and beta=2cos^(-1)(1/3) then which of the foll...

    Text Solution

    |

  12. For a continuous function f(x), equation f(x)=0 has 4 distinct solutio...

    Text Solution

    |

  13. Which of the following functions is/are injective function (s) in the...

    Text Solution

    |

  14. Consider f(x)={("min"(|x|sqrt(1-x^(2))),,,-1lexle1),([|x|],,,1lt|x|lt2...

    Text Solution

    |

  15. If f(x)={((sinx+cosx)^(cosecx),-(pi)/2ltxlt0),(a,x=0),((e^(1/x)+e^(2/x...

    Text Solution

    |

  16. If f(x) is a monic polynomial of degree '3' such that lim(x to 0) (1+f...

    Text Solution

    |

  17. If f(x) is a monic polynomial of degree '3' such that lim(x to 0) (1+f...

    Text Solution

    |

  18. Let there are two functions defined of f(x)="min"{|x|,|x-1|} on the...

    Text Solution

    |

  19. Let there are two functions defined of f(x)="min"{|x|,|x-1|,|x+1+] ...

    Text Solution

    |

  20. There are positive integer x and y satisfying system of equations lo...

    Text Solution

    |