Home
Class 12
MATHS
The function f:R to R is defined by f(x)...

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

A

`((3)/(4),1]`

B

`[(3)/(4),1)`

C

`[(3)/(4),1]`

D

`((3)/(4),1)`

Text Solution

Verified by Experts

The correct Answer is:
C
`y=f(x)=cos^(2)x+sin^(4)x`
`=cos^(2)x+sin^(2)x(1-cos^(2)x)`
`=cos^(2)x+sin^(2)x-sin^(2)x cos^(2)x`
`=1-sin^(2)x cos^(2)x`
`=1-(1)/(4) sin^(2)2x`
` :. (3)/(4) le f(x) le 1 " " ( :' 0 le sin^(2)2x le 1)`
` :. f(x) in [3//4,1]`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 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)

Let a function f:R to R be defined by f(x)=2x+cosx+sinx " for " x in R . Then find the nature of f(x) .

If the function f: R to R is defined by f(x) =(x^(2)+1)^(35) for all x in RR then f is

Let the function f:R to R be defined by f(x)=x+sinx for all x in R. Then f is -

If f : R rarr R is defined by f(x)=1/(2-cos3x) for each x in R , then the range of f is

If f:R to R be defined by f(x) =2x+sinx for x in R , then check the nature of the function.

Let the function f : R to R be defined by f(x)= 2x + cos x , then f(x)-

If the function f: R to R is defined by f(x)=x^(2)-6x-14 , then f^(-1)(2) is equal to -

Let f : R to R be defined as f(x) = (x^2-x+4)/(x^2+x+4) . Then the range of the function f(x) is

Draw the graph of the function f: R to R defined by f(x)=x^(3), x in R .

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. If x is real, then the value of the expression (x^2+14 x+9)/(x^2+2x+3)...

    Text Solution

    |

  2. Find the range of the following function f(x)=|x-1|+|x-2|,-1lexle3 is

    Text Solution

    |

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

    Text Solution

    |

  4. The range of f(x)=[|sin x|+|cosx"|""]"dot Where [ ] denotes the greate...

    Text Solution

    |

  5. The range of given function f(x)=^(7-x)P(x-3) is given by

    Text Solution

    |

  6. The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is (a)[0,pi/2] (b) (0,pi/...

    Text Solution

    |

  7. If the function f:R rarr A is given by f(x)=(e^x-e^(-|x|))/(e^x+e^(|x|...

    Text Solution

    |

  8. Domain (D) and range (R) of f(x)=sin^(-1)(cos^(-1)[x]), where [.] deno...

    Text Solution

    |

  9. The range of the function f defined by f(x)=[1/(sin{x})] (where [.] an...

    Text Solution

    |

  10. Range of function f(x) = cos (k sin x) is [-1, 1], then the least posi...

    Text Solution

    |

  11. Let f(x)=sqrt(|x|-|x+)(w h e r e{dot} denotes the fractional part of (...

    Text Solution

    |

  12. The range of f(x)=cos^(-1)((1+x^3)/(x2))+sqrt(2-x^2) is {0,1+pi/2} (b...

    Text Solution

    |

  13. The range of the following function is f(x)=sqrt((1-cosx)sqrt((1-cosx)...

    Text Solution

    |

  14. The range of f(x)=(x+1)(x+2)(x+3)(x+4)+5 for x in [-6,6] is [4, 5045] ...

    Text Solution

    |

  15. The range of f(x)=sec^(-1)((log)3tanx+(log)(tanx)3) is (a) [pi/3,pi/2...

    Text Solution

    |

  16. The domain of definition of the function f(x)={x}^({x})+[x]^([x]) is w...

    Text Solution

    |

  17. 49. If [x^2-2x + a] = 0 has no solution then

    Text Solution

    |

  18. The value of sum(r=1)^(2000) {{x+r}}/2000 is

    Text Solution

    |

  19. If f(x)=(sin([x]pi))/(x^2+x+1) , where [dot] denotes the greatest inte...

    Text Solution

    |

  20. Let f(x)=([a]^2-5[a]+4)x^3-(6{a}^2-5{a}+1)x-(tanx)xsgnx be an even fun...

    Text Solution

    |