Home
Class 12
MATHS
let the function f be defined by f (x)= ...

let the function f be defined by `f (x)= {{:(p+ qx+ x^(2)"," , x lt 2),( 2 px+3qx ^(2)"," , x ge 2):},` Then:

A

`f(x)` is continuous in `R` if `2p+5q=4`

B

`f(x)` is differentiable in `R` if `p!=q`

C

`f(x)` is differentiable in `R` if `p=q=4/13`

D

if `p=-2` and `q=3` then `f(x)` is continuous in `R`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Let f:RtoR is given by f(x)={(p+qx+x^(2),xlt2),(2px+3qx^(2),xge2):} then:

Let a function f be defined as f(x) = {:{(x," if " 0 le x lt 1/2),(0," if "x=1/2),(x-1," if" 1/2 lt x le 1):} Establish the existence of Lim_(x to 1/2) f(x) .

What is the range of the function f that is defined by f(x) = {{:(3^((1)/(x^(2)+1))", if " x ge 0),(5x+3", if " x lt 0):} ?

Find the values of a and b such that the function defined by f(x)={{:(5, if xle2), (a x+b , if 2 lt x lt10 ),(21 , ifx ge10):} is a continuous function.

Find the values of a and b such that the function defined by is continuous. f(x) = {(x^(2)+1","," "xle 2),(ax + b",", 2 lt x lt 10),(2x+1",", " "x ge 10):}

For what values of p does the Lim_(x to 1) f(x) exist , where f is defined by the rule f(x) = {:{(2px+3," if " x lt 1 ),(1 - px^(2)," if "x gt 1):}

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

If f:R to R is defined as: f(x)= {{:(2x+1, "if",x gt 2),(x^(2)-1,"if",-2 lt x lt 2),(2x,"if",x lt -2):} then evaluate the following: (i) f(1) (ii) f(5) (iii) f(-3)

A function is defined as follows f(x)={:{(x^(3),, x^(2)lt1),(x, , x^(2)ge 1):} then function is

Let f:R->R be a function defined by f(x)=x^2-(x^2)/(1+x^2) . Then:

ALLEN-TEST PAPERS-MATHEMATICS
  1. f:RtoR is defined as f(x)=x^(3)+2x^(2)+7x+cos(pix) and g be the invers...

    Text Solution

    |

  2. y=sinx+e^(x) then (d^(2)x)/(dy^(2)) is:

    Text Solution

    |

  3. Let f(x) be a cubic polynomical such that f'(x)=0 at x=1 and x=3, f(1)...

    Text Solution

    |

  4. lim(xto oo)(ln(x^(2)+5x)-2ln(cx+1)=-2 then

    Text Solution

    |

  5. The variable x satisfying the equation |sinxcosx|+sqrt(2+tan^2+cot^2x)...

    Text Solution

    |

  6. The quadratic polynomial p(x) has the following properties:p(x)geq0 fo...

    Text Solution

    |

  7. Number of points on [0,2] where f(x)={(x{x}+1,(0lexlt1),(2-{x},1lex...

    Text Solution

    |

  8. Let sin theta-cos theta=1 then the value of sin^(3) theta-cos^(3)theta...

    Text Solution

    |

  9. Domain off(x)=log(x^2+5x+6)/([x]-1)where [.] denotes greatest integer ...

    Text Solution

    |

  10. The vaue of x satisfying sin^(-1)(x)+sin^(-1)(sqrt(15)x)=(pi)/2 is

    Text Solution

    |

  11. The sum sum(n=1)^oo tan^(-1)(3/(n^2+n-1)) is equal to

    Text Solution

    |

  12. Range of f(x)=sin^(-1)x+tan^(-1)x+sqrt(x+1) is [a,b] then b+a is equal...

    Text Solution

    |

  13. Let f(x)={(cos[x],xge0),(|x|+a,xlt0):} (where [.] denotes greatest i...

    Text Solution

    |

  14. The reciprocal of the value of underset(ntooo)lim(1-(1)/(2^(2)))(1-(...

    Text Solution

    |

  15. The velue of lim(x->0)(sin(3sqrtx)ln(1+3x))/((tan^(- 1)sqrt(x))^2(e^(...

    Text Solution

    |

  16. lim(xto0)(3-3tan((pi)/4-x))/(sin2x) is equal to

    Text Solution

    |

  17. let the function f be defined by f (x)= {{:(p+ qx+ x^(2)"," , x lt 2),...

    Text Solution

    |

  18. Let h (x) = min (x, x^2), x in R, then h (x) is

    Text Solution

    |

  19. The number of points where the function f(x)={{:(1+[ cos ""(pix)...

    Text Solution

    |

  20. f(x)={(x^(2)e^(1//x),x!=0),(0,x=0):} then left hand derivative at x=0 ...

    Text Solution

    |