Home
Class 12
MATHS
f:R to R is defined as f(x)= {{:(x^(2)+k...

`f:R to R` is defined as `f(x)= {{:(x^(2)+kx+3",",,"for "xge0),(2kx+3",",,"for "x lt0):}`. If `f(x)` is injective, then find the values of `k`.

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVE

    BANSAL|Exercise All Questions|376 Videos
  • INTEGRALS

    BANSAL|Exercise All Questions|111 Videos

Similar Questions

Explore conceptually related problems

If f:R to R is defined by f(x) = x^(2)-3x+2, write f{f(x)} .

If f(x)={(kx+2,,x 5) is continuous, then value of k is

f:R rarr Rf:R rarr R is defined by f(x)=x^(2)-3x+2 find

Let f:R rarr R be defined as f(x)={2kx+3,x =0 If f(x) is injective then find the smallest integral value of

If f:R rarr R is defined by f(x)=3x-2 then f(f(x))+2=

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)

If f:R rarr R is defined by f(x)=3x+2 define f[f(x)]

If f: R->R is defined by f(x)=3x+2 , find f(f(x)) .

Let f:R rarr R be defined by f(x)={x+2x^(2)sin((1)/(x)) for x!=0,0 for x=0 then

Let f: R to R be defined as f(x)={{:(x^(5) sin""((1)/(x))+5x^(2)",",x lt0),(" 0,", x=0),(x^(5) cos""((1)/(x))+ lambdax^(2)",",x gt 0):} The value of lambda for which f''(0) exists , is ____________

BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. (lim)(x->\ 0)(cosx)^(cot2x) equals

    Text Solution

    |

  2. Evaluate the following limit: (lim)(x->pi/4)(1-t a n x)/(x-pi/4)

    Text Solution

    |

  3. f:R to R is defined as f(x)= {{:(x^(2)+kx+3",",,"for "xge0),(2kx+3",",...

    Text Solution

    |

  4. If (lim)(x->2)(f(x-9))/(x-2)=3 then (lim)(x->2)f(x), is

    Text Solution

    |

  5. If (lim)(x->oo)(7^(k x)+8)/(7^(5x)+6) does not exist then' k ' c...

    Text Solution

    |

  6. L i m i t\ l=(lim)(x->oo)(pi/2-t a n^-1\ x)/(ln(1-1/x)) equals

    Text Solution

    |

  7. lim(x->oo)((2x+1)^(40)(4x-1)^5)/((2x+3)^(45))=

    Text Solution

    |

  8. Evaluate the following limit : (lim)(x->oo)(logx)/(x^n),\ n >0

    Text Solution

    |

  9. Evaluate the following limit : (lim)(x->-oo)(sqrt(4x^2+5x+8))/(4x+5...

    Text Solution

    |

  10. Evaluate the following limit : (lim)(n->oo)(n/(n+y))^n

    Text Solution

    |

  11. Evaluate the following limit : (lim)(x->0)((4^x-1)^3)/(sin((x^2)/4)l...

    Text Solution

    |

  12. Evaluate underset(xto0)lim(sinx^(0))/(x).

    Text Solution

    |

  13. Evaluate ("lim")(nvecoo){cos(x/2)cos(x/4)cos(x/8) cos(x/(2^n))}

    Text Solution

    |

  14. Evaluate: ("lim")(hvec0)(2[sqrt(3)sin(pi/6+h)-cos(pi/6+h)])/(sqrt(3)h(...

    Text Solution

    |

  15. Evaluate the following limit : (lim)(x->oo)((1-cos2x)sin5x)/(x^2sin3...

    Text Solution

    |

  16. Evaluate the following limit : (lim)(alpha->beta)[(sin^2alpha-sin^2b...

    Text Solution

    |

  17. Evaluate the following limit : (lim)(x->0)((a^x+b^x+c^x)/3),\ (a , ...

    Text Solution

    |

  18. Evaluate the following limit (lim)(x->oo)((3x-4)/(3x+2))^((x+1)/3)

    Text Solution

    |

  19. Evaluate the following limit (lim)(x->oo)((x+3)/(x+1))^(x+1)

    Text Solution

    |

  20. Evaluate the following limit (lim)(x->oo)(1+a x)^(1/x)

    Text Solution

    |