Home
Class 12
MATHS
Let f(x)={(2x+a",",x ge -1),(bx^(2)+3","...

Let `f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):}`
and `g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):}`
`g(f(x))` is not defined if

A

`a in (10,oo), b in (5,oo)`

B

`a in (4,10), b in (5,oo)`

C

`a in (10,oo), b in (0,1)`

D

`a in (4,10), b in (1, 5)`

Text Solution

Verified by Experts

The correct Answer is:
A
`g(f(x))` is not defined if
(i) `-2+a gt 8 and " (ii) "b+3 gt 8`
`or a gt 10 and b gt 5`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Matrix)|9 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Numerical)|31 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|31 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} If a=2 and b=3, then the range of g(f(x)) is

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

Consider the functions f(x)={(x+1",",x le 1),(2x+1",",1lt x le 2):} and g(x)={(x^(2)",", -1 le x lt2),(x+2",",2le x le 3):} The domain of the function f(g(x)) is

Consider the functions f(x)={(x+1",",x le 1),(2x+1",",1lt x le 2):} and g(x)={(x^(2)",", -1 le x lt2),(x+2",",2le x le 3):} The range of the function f(g(x)) is

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=

The function f(x)= {(5x-4 ", " 0 lt x le 1 ),( 4x^3-3x", " 1 lt x lt 2):}

If f(x) ={(4-3x,",",0 lt x le 2),(2x-6,",",2 lt x le 3),(x+5,",",3 lt x le 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)={{:(x^(2)-4x+3",", x lt 3),(x-4",", x ge 3):} and g(x)={{:(x-3",", x lt 4),(x^(2)+2x+2",", x le 4):} , which one of the following is/are true?

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Comprehension)
  1. If a0 = x,a(n+1)= f(an), where n = 0, 1, 2, ..., then answer thefoll...

    Text Solution

    |

  2. If a(0)=x,a(n+1)=f(a(n)), " where " n=0,1,2, …, then answer the follow...

    Text Solution

    |

  3. If a(0)=x,a(n+1)=f(a(n)), " where " n=0,1,2, …, then answer the follow...

    Text Solution

    |

  4. Let f(x)=f1(x)-2f2 (x), where ,where f1(x)={((min{x^2,|x|},|x|le 1),(...

    Text Solution

    |

  5. Let f(x)=f(1)(x)-2f(2)(x), where where f(x)={(min{x^(2)","|x|}",",|x...

    Text Solution

    |

  6. Let f(x)=f1(x)-2f2 (x), where ,where f1(x)={((min{x^2,|x|},|x|le 1),(...

    Text Solution

    |

  7. Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",...

    Text Solution

    |

  8. Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",...

    Text Solution

    |

  9. Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",...

    Text Solution

    |

  10. Let f : R -> R is a function satisfying f(2-x) = f(2 + x) and f(20-x)...

    Text Solution

    |

  11. Let f:R to R be a function satisfying f(2-x)=f(2+x) and f(20-x)=f(x) ...

    Text Solution

    |

  12. Let f:R to R be a function satisfying f(2-x)=f(2+x) and f(20-x)=f(x) ...

    Text Solution

    |

  13. Consider two functions f(x)={([x]",",-2le x le -1),(|x|+1",",-1 lt x...

    Text Solution

    |

  14. Consider two functions f(x)={([x]",",-2le x le -1),(|x|+1",",-1 lt x...

    Text Solution

    |

  15. Consider two functions f(x)={([x]",",-2le x le -1),(|x|+1",",-1 lt x...

    Text Solution

    |

  16. Consider a function f whose domain is [-3, 4] and range is [-2, 2] wit...

    Text Solution

    |

  17. Consider a function f whose domain is [-3, 4] and range is [-2, 2] wit...

    Text Solution

    |

  18. Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f...

    Text Solution

    |

  19. Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f...

    Text Solution

    |

  20. Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f...

    Text Solution

    |