Home
Class 12
MATHS
Let f(x) = {(x^(2)-a, if x lt 3),(bsqrt(...

Let `f(x) = {(x^(2)-a, if x lt 3),(bsqrt(x-2)+a, if 3 le x lt 6),(2x+b, if x ge 6):}` If f(x) is continuous `AA x in R` then the value of f(1)+f(3)+f(7), is

Text Solution

Verified by Experts

The correct Answer is:
45
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    CENGAGE|Exercise Solved Examples And Exercises|108 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|91 Videos

  • COORDINATE SYSTEM

    CENGAGE|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

f(x)={{:(|x|+3, if x le -3),(-2x, if -3 lt x lt 3 ),(6x + 2, if x ge3):}

If f(x) {:(=x^(2)-1", if "x lt 3 ),(= 2ax ", if "x le 3 ) :} is continuous at x = 3 , then a = ……

f(x)={(|x|+3",","if", x le -3),(-2x",", "if", -3 lt x lt 3),(6x+2",","if",x ge 3):} is

show that f(x) ={{:( (2x-1)",",if , x lt2),( (3x)/2",,if x ge 2):} is continuous

Let f(x)={{:(ax-b,","x le 1),(3x,"," 1 lt x lt 2),(bx^2-a,"," x ge 2):} If f is continuous function then (a,b) is equal to

Let f(x)={{:(x^(3)-1",", x lt2),(x^(2)+3"," , x ge 2):} Then

Let f (x)= {{:(x ^(2),0lt x lt2),(2x-3, 2 le x lt3),(x+2, x ge3):} then the tuue equations:

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, if , x ge 1),( x^(2), if , x lt 1):} is f a continuous function ? Why ?

CENGAGE-CONTINUITY AND DIFFERENTIABILITY-Question Bank
  1. Let f(x) = {(x^(2)-a, if x lt 3),(bsqrt(x-2)+a, if 3 le x lt 6),(2x+b,...

    Text Solution

    |

  2. Given f(x) = {(x^(2)-5x+alpha, -ooltxle 0),(|7-3x|+sin [x], o lt x lt ...

    Text Solution

    |

  3. Let f(x) = {(sqrt(x^(2)-1), x le sqrt10),((sqrt(10x)-7), sqrt10lt xlt...

    Text Solution

    |

  4. Let f(x) = sqrt(x^(2)+px+1)/(x^(2)-p). If f(x) is discontinuous at exa...

    Text Solution

    |

  5. Number of points of non-derivability of the function f(x) = root (3)((...

    Text Solution

    |

  6. If f(x) = {(lim(x rarr oo)(6^(t)+10^(t))^(1/t), x = 0),(x^(2)+4x+C, x ...

    Text Solution

    |

  7. Number of point(s) in [1,2] where f(x) = (-2)^([x^(3)]) is non-differe...

    Text Solution

    |

  8. Consider the function f(x) = {(a^(2)+e^(x), -oo lt x lt 0),(x+2, 0le x...

    Text Solution

    |

  9. Let f(x) = [(sqrt(1+sin^(2)(x^(2))-cos^(3)(x^(2)))/(x^(3)tanx), if x n...

    Text Solution

    |

  10. Let f(x) = {(cos(x^(3)), -ooltxlt0),(sin(x^(3))-|x^(3)-1|, 0lexltoo):}...

    Text Solution

    |

  11. The sum of all values of x for which the function f(x) = sqrt(|x^(2)-5...

    Text Solution

    |

  12. Let f(x) = [(-1, -3 le x lt 0),(x-1, 0le xle 3):} and g(x) = f(|x|)+|f...

    Text Solution

    |

  13. Let f(x) be a differentiable function satisfying f((x+2y)/3)= (f(x)+2f...

    Text Solution

    |

  14. Let f(x) = {((sin alphax^(2))/x^(2), x ne 0),(3/4+1/(4alpha), x = 0):}...

    Text Solution

    |

  15. Let f(x) = {(a tan^(-1)(1/(x-4)), 0 lexlt4),(pi/2, x= 4),(btan^(-1)(2/...

    Text Solution

    |

  16. Let f(x) = {((1+ax)^(1/x), x lt 0),((root(3)(x+c)-1)/(sqrt(x+1)-1), x ...

    Text Solution

    |

  17. The number of points in (-5,5) where f(x)=[x](x^(3)-x)^(2)) is non-dif...

    Text Solution

    |

  18. If f(x) = cos (x (cos)1/x) and g(x) = (In(sec^(2)x))/(x sin x) are bot...

    Text Solution

    |

  19. Consider , f(x) = {(|(x-x^(3) 1 2),(0 2 3x^(4)),(x^(2) 4x x^(3)-3x^(5)...

    Text Solution

    |

  20. Number of points where f(x)= max {2-|x|, min {x^(2)-1}} is not differe...

    Text Solution

    |