Home
Class 12
MATHS
Find the range of f(x)=|sinx|+|cosx|,x i...

Find the range of `f(x)=|sinx|+|cosx|,x in Rdot`

Text Solution

Verified by Experts

`f(x)=|sinx|+|cosx|, x in R`.
Clearly, `f(x) gt 0`.
Also, `f^(2)(x)=sin^(2)x+cos^(2)x+|2 sinx cos x|=1+|sin2x|`
Now, `0 le |sin zx|le1`
` :. 1 le 1 +|sin zx| le 2`
` :. 1 le f^(2)(x) le 2`
or ` 1 le f(x) le sqrt(2)`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.1|15 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.2|5 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise JEE Previous Year|12 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|28 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Find the range of f(x)=sin(cosx).

Find the range of f(x) =8/(sinx+3)

Find the range of f(x)=1/(5sinx-6)

Find the range of f(x)=(log)_esinx

Find the range of f(x)=sin^2x-3sinx+2

Find the range of f(x)=sin^2x-sinx+1.

Find the range of f(x)=x^2-x-3.

Find the range of f(x)=1/(2cosx-1)

Find the range of f(x)=1/(4cosx-3)dot

find the range of f(x)=(1)/(1+4cosx)

CENGAGE-RELATIONS AND FUNCTIONS-Examples
  1. Find the range of the function f(x)=3 sin (sqrt((pi^(2))/(16)-x^(2))).

    Text Solution

    |

  2. if:f(x)=(sinx)/(sqrt(1+tan^2x))-(cosx)/(sqrt(1+cot^2x)), then find the...

    Text Solution

    |

  3. Find the range of f(x)=|sinx|+|cosx|,x in Rdot

    Text Solution

    |

  4. Find the range of f(theta)=5costheta+3cos(theta+pi/3)+3

    Text Solution

    |

  5. Solve sinx >-1/2or find the domain of f(x)=1/(sqrt(1+2sinx))

    Text Solution

    |

  6. Find the number of solutions of sinx=x/(10)

    Text Solution

    |

  7. Find the number of solutions of the equation sinx=x^2+x+1.

    Text Solution

    |

  8. Find the domain and range of the function f(x)="sin"^(-1)(x^(2))/(2)

    Text Solution

    |

  9. Domain of the function f(x)=sin^(- 1)(1+3x+2x^2)

    Text Solution

    |

  10. Find the values of x for which the following pair of functions are ide...

    Text Solution

    |

  11. Find the domain and range of the function f(x) = sin^(-1)((1+e^(x))^(-...

    Text Solution

    |

  12. Find the domain for f(x)=sin^(-1)((1+x^2)/(2x))

    Text Solution

    |

  13. Find the range of f(x)=sin^(-1)x+tan^(-1)x+cos^(-1)xdot

    Text Solution

    |

  14. Find the domain of f(x)=sqrt(cos^(-1)x-sin^(-1)x)

    Text Solution

    |

  15. Find the range of tan^(-1)((2x)/(1+x^2))

    Text Solution

    |

  16. Find the range of f(x)=cot^(-1)(2x-x^2)dot

    Text Solution

    |

  17. Find the range of f(x)=cos^(-1)((sqrt(1+2x^2))/1)

    Text Solution

    |

  18. Find the domain of f(x)=sqrt(((1-5^x)/(7^(-1)-7)))

    Text Solution

    |

  19. Find the domain of f(x)=sqrt((0. 625)^(4-3x)-(1. 6)^(x(x+8)))

    Text Solution

    |

  20. Is the pair of the functions e^(sqrt(log(e)x)) and sqrt(x) identical ?

    Text Solution

    |