Home
Class 11
MATHS
The function f: R ⇒ R is defined by f(x)...

The function `f: R ⇒ R` is defined by `f(x)=cos^2x+sin^4x , r a n g e o f f(x)=` (a)`[3//4,1)` (b) `(3//4,1]` (c) `[3//4,1]` (d) (`3//4,1)`

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

The function f: R-R is defined by f(x)=cos^2x+sin^4xforx in Rdot Then the range of f(x) is (3/4,1] (b) [3/4,1) (c) [3/4,1] (d) (3/4,1)

The function f:R→R defined by f(x)=(x−1)(x−2)(x−3) is

The function f:R to R is defined by f(x)=cos^(2)x+sin^(4)x for x in R . Then the range of f(x) is

The function f : R -> R is defined by f (x) = (x-1) (x-2) (x-3) is

Consider a function f:R rarr R defined by f(x)=x^(3)+4x+5 , then

The function f:R rarr R defined as f(x)=(3x^2+3x-4)/(3+3x-4x^2) is :

A function f: R to R is defined as f(x)=4x-1, x in R, then prove that f is one - one.

If f(x)=sin^6x+cos^6x , then range of f(x) is [1/4,1] (b) [1/4,3/4] (c) [3/4,1] (d) none of these

If f(x)=sin^6x+cos^6x , then range of f(x) is [1/4,1] (b) [1/4,3/4] (c) [3/4,1] (d) none of these

Let f: R->R be defined by f(x)=x^4 , write f^(-1)(1) .

RD SHARMA ENGLISH-FUNCTIONS-All Questions
  1. If f is a real valued function given by f(x)=27 x^3+1/(x^3)a n dalpha,...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. Find the domain of definition of the function f(x) given by f(x)=1/(lo...

    Text Solution

    |

  20. Find the range of each of the following functions: f(x)=|x-3| f(x)=...

    Text Solution

    |