Home
Class 12
MATHS
f(x)=x^(3)+3x^(2)+4x+bsinx+c cosx,forall...

`f(x)=x^(3)+3x^(2)+4x+bsinx+c cosx,forall x in R` is a one-one function, the value of `b^(2)+c^(2)` is

A

(a)1

B

(b)2

C

(c)`sqrt(2)`

D

(d)None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|25 Videos
  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos
  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 12|4 Videos
  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos
  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

If f(x)=x^3+3x^2+4x+ bsinx+ c cosx AA x in R is a one-one function then the value of b^2 + c^2 is

Let f:R rarr R and f(x)=(3x^(2)+mx+n)/(x^(2)+1) . If the range of this function is [-4,3] , then the value of (m^(2)+n^(2))/(4) is ….

The function f(x)=(4-x^(2))/(4x-x^(3)) is

If f:[-20,20]->R defined by f(x)=[x^2/a]sinx+cosx is an even function, then set of values of a is

Let f(x)=x+2|x+1|+x-1| . If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 2

Let f (x) be a real vaued continuous function such that f (0) =1/2 and f(x+y) = f(x) f (4-y) + f(y) f (4-x ) AA x, y in R, then for some real a: a. f(x) is a periodic function b. f(x) is a constant function c. f(x)=1/2 d. f(x)=(cosx)/2

If f:R to R be defined by f(x) =2x+sinx for x in R , then check the nature of the function. a. one-to-one and onto b. one-to-one but not onto c. onto but not one-to-one d. neither one-to-one nor onto

Which of the following functions are one-one? f(x) = 2x^2 + 3

Let f(x)= |{:(cosx,sinx,cosx),(cos2x,sin2x,2cos2x),(cos3x,sin3x,3cos3x):}| then find the value of f'((pi)/(2)) .

ARIHANT MATHS-FUNCTIONS-Exercise (Single Option Correct Type Questions)
  1. Let f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-(x))dot Show that g(...

    Text Solution

    |

  2. If f(x) and g(x) are non-periodic functions, then h(x)=f(g(x)) is

    Text Solution

    |

  3. If f(x) is a real-valued function discontinuous at all integral points...

    Text Solution

    |

  4. A function f from integers to integers is defined as f(x)={{:(n+3, n ...

    Text Solution

    |

  5. If f:R->R and f(x)=sin(pi{x})/(x^4+3x^2+7), where {} is a fractional p...

    Text Solution

    |

  6. Show that f: R→ R defined as f(a) = 3a – 4 is one to one function.

    Text Solution

    |

  7. Find dy/dx if y= 3^x

    Text Solution

    |

  8. Let y be element of the set A={1,2,3,,5,6,10,15,30} and x(1),x(2),x(3)...

    Text Solution

    |

  9. If A gt 0, c,d,u.v are non-zero constants and the graph of f(x)=abs(Ax...

    Text Solution

    |

  10. f(x)=x^(3)+3x^(2)+4x+bsinx+c cosx,forall x in R is a one-one function,...

    Text Solution

    |

  11. If two roots of the equation (p-1)(x^2 +x +1)^2 -(p+1)(x^4+x^2+1)=0 ar...

    Text Solution

    |

  12. If f(x)=x^11+x^9−x^7+x^3+1 and f(sin^(−1)(sin8))=α,α is constant, then...

    Text Solution

    |

  13. Let f(x)=sin^(-1)2x + cos^(-1)2x + sec^(-1)2x. Then the sum of the max...

    Text Solution

    |

  14. The complete set of values of a for which the function f(x)=tan^(-1)(x...

    Text Solution

    |

  15. The domain of the function f(x)=sin^(-1)""(1)/abs(x^(2)-1)+1/sqrt(si...

    Text Solution

    |

  16. The domain of f(x)=(log(sin^(-1)sqrt(x^(2)+x+1)))/(log(x^(2)-x+1)) is ...

    Text Solution

    |

  17. The domain of f(x)=sqrt(sin^(-1)(3x-4x^(3)))+sqrt(cos^(-1)x) is equal ...

    Text Solution

    |

  18. The domain of the function f(x)=root(6)(4^(x)+8^(2//3(x-2))-52-2^(2(...

    Text Solution

    |

  19. The domain of derivative of the function f(x)=abs(sin^(-1)(2x^(2)-1)...

    Text Solution

    |

  20. The range of a function f(x)=tan^(-1){log(5//4)(5x^(2)-8x+4)} is

    Text Solution

    |