Home
Class 11
MATHS
If f is a real valued function given by ...

If `f` is a real valued function given by `f(x)=27 x^3+1/(x^3)a n dalpha,beta` are roots of `3x+1/x=2.` Then, `f(alpha)=f(beta)=-9` (b) `f(alpha)=10` (c) `f(beta)=-10` (d) none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    RD SHARMA ENGLISH|Exercise All Questions|100 Videos
  • GEOMETRIC PROGRESSIONS

    RD SHARMA ENGLISH|Exercise All Questions|256 Videos

Similar Questions

Explore conceptually related problems

If f (x) = 27x^(3) -(1)/(x^(3)) and alpha, beta are roots of 3x - (1)/(x) = 2 then

If f(x)=64x^3+1/x^3 and alpha,beta are the roots of 4x+1/x=3 . Then,value of f(x)=

If alpha,\ beta are the zeros of the polynomial f(x)=x^2+x+1 , then 1/alpha+1/beta= (a) 1 (b) -1 (c) 0 (d) None of these

Let f(x) be a second degree polynomial function such that f(-1)=f(1) and alpha,beta,gamma are in A.P. Then, f'(alpha),f'(beta),f'(gamma) are in

If alpha,\ beta are the zeros of polynomial f(x)=x^2-p(x+1)-c , then (alpha+1)(beta+1)= (a) c-1 (b) 1-c (c) c (d) 1+c

If alpha and beta are roots of the equation 2x^(2)-3x-5=0 , then the value of (1)/(alpha)+(1)/(beta) is

If f(x)=(cotx)/(1+cotx)andalpha+beta=(5pi)/(4) , then find f(alpha).f(beta) .

If alpha,beta are zeroes of polynomial f(x) =x^(2)-p(x+1)-c , then find the value of (alpha+1)(beta+1) .

If f(x)=a=b x+c x^2a n dalpha,beta,gamma are the roots of the equation x^3=1,t h e n|a b c b c a c a b| is equal to f(alpha)+f(beta)+f(gamma) f(alpha)f(beta)+f(beta)f(gamma)+f(gamma)f(alpha) f(alpha)f(beta)f(gamma) -f(alpha)f(beta)f(gamma)

Let f(x)=ax^3+bx^2+cx+1 has exterma at x=alpha,beta such that alpha beta 0 (c)one positive root if f(alpha) 0 (d) none of these

RD SHARMA ENGLISH-FUNCTIONS-All Questions
  1. Find the domain and range of the function f(x)=1/(2-sin3x) .

    Text Solution

    |

  2. If [x]^2-5[x]+6=0, where [.] denotes the greatest integer function, th...

    Text Solution

    |

  3. If f is a real valued function given by f(x)=27 x^3+1/(x^3)a n dalpha,...

    Text Solution

    |

  4. If 3f(x)+5f(1/x)=1/x-3 for all non-zero x , then f(x)= (a)1/(16)(...

    Text Solution

    |

  5. The function f: R ⇒ R is defined by f(x)=cos^2x+sin^4x , r a n g e ...

    Text Solution

    |

  6. If e^(f(x))=(10+x)/(10-x),x in (-10 ,10)a n df(x)=kf((200 x)/(100+x^2)...

    Text Solution

    |

  7. The domain of definition of f(x)=sqrt((x+3)/((2-x)(x-5))) is (a)(-oo,-...

    Text Solution

    |

  8. The range of the function f(x)=sqrt(5|x| - x^2 - 6) is equals to ...

    Text Solution

    |

  9. If f: R \rightarrow R be given by f(x)=(4^x)/(4^x+2) for all x in Rdo...

    Text Solution

    |

  10. If f(x)=sin[pi^2]x+sin[-pi^2]x, where [x] denotes the greatest integer...

    Text Solution

    |

  11. If f is a real function defined by f(x)=(x-1)/(x+1), then prove that f...

    Text Solution

    |

  12. If y=f(x)=(a x-b)/(b x-a) , show that x=f(y)dot

    Text Solution

    |

  13. If f(x)=(x-1)/(x+1),x!=-1, . then show that f(f(x))=-1/x , prove that ...

    Text Solution

    |

  14. t f be defined by f(x)=x-4 and g be defined by g(x)={(x^2-16)/(x+4)...

    Text Solution

    |

  15. Express the function f: X->R given by f(x)=x^3+1 as set of ordered pai...

    Text Solution

    |

  16. If f(x)=x+1/x , prove that [f(x)]^3=f(x^3)+3f(1/x)dot .

    Text Solution

    |

  17. Let f: RvecRa n dg: CvecC be two functions defined as f(x)=x^2a n dg(x...

    Text Solution

    |

  18. Let A={12 ,13 ,14 ,15 ,16 ,17}a n df: A→Z be function given by f(x)= h...

    Text Solution

    |

  19. Find the domain of each of the following functions given by f(x)=1/(sq...

    Text Solution

    |

  20. Find the domain of definition of the following f(x) given by f(x)=log4...

    Text Solution

    |