Home
Class 12
MATHS
The range of the function is f(x)=log5(2...

The range of the function is `f(x)=log_5(25-x^2)` is

A

`[0, 5]`

B

` [0, 2)`

C

` (0, 2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Cleary, f(x) is defined, if
`25-x^(2) gt 0 rArr - 5 lt x lt 5`
Now, let `y = log_(5) (25-x^(2))`. Then
`5^(y) = 25- x^(2) rArr - 5 lt x lt 5`
For x to real, we must have
`25-5^(y) ge 0 rArr 5^(y) le 25 rArr y le 2`
Also, `y =f(x) to - oo` as `x to pm5`.
Hence, range `(f) = (-oo,2]`
Promotional Banner

Topper's Solved these Questions

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|8 Videos

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|94 Videos

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|55 Videos

  • SCALAR AND VECTOR PRODUCTS OF THREE VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|63 Videos

Similar Questions

Explore conceptually related problems

The range of the function f(x)=(5)/(3-x^(2)) is

The range of the function f(x) = log_(3) (5+4x - x^(2)) , is

The range of the function f(x)=5-4x-x^(2) is

The range of the function f(x)=(x^(2)-2)/(x^(2)-3) is

Find the range of the functions: f(x)=2-3x-5x^(2)

The range of the function f(x)=sqrt(1-x^2)/(1+|x|) is

The range of the function f(x)=cos^(2)x -5 cosx -9 is :

The range of the function f(x)=x^2+1/(x^2+1) is

The range of the function f(x)=x^2+1/(x^2+1) is

The range of the function f(x) = (1)/(2-sin 3x) is

OBJECTIVE RD SHARMA ENGLISH-REAL FUNCTIONS -Section I - Solved Mcqs
  1. The range of the function f(x)=(1)/(2-cos 3x) is

    Text Solution

    |

  2. The range of the function f(x) = log(3) (5+4x - x^(2)), is

    Text Solution

    |

  3. The range of the function is f(x)=log5(25-x^2) is

    Text Solution

    |

  4. The range of function f:[0,1] to R , f(x) = x^3-x^2 + 4x + 2 sin^(-1) ...

    Text Solution

    |

  5. Let f(x)=4 cos sqrt(x^(2)-pi^(2)/9). Then, the range of f(x) is :

    Text Solution

    |

  6. The range of the function f(x) = tan sqrt((pi^(2))/(9)-x^(2)), is

    Text Solution

    |

  7. Let f(x)=sec^(-1)[1+cos^(2)x], where [.] denotes the greatest integer ...

    Text Solution

    |

  8. The range of the function f(x) = sqrt(2-x)+sqrt( 1+x)

    Text Solution

    |

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

    Text Solution

    |

  10. If f(x) is a periodic function with period lambda and f(ax+b) is perod...

    Text Solution

    |

  11. The peroid of the function f(x) = |cos.(x)/(2)|+ |sinx| is

    Text Solution

    |

  12. Let f(x) = x(2-x), 0 le x le 2. If the definition of f(x) is extende...

    Text Solution

    |

  13. The peroid of the function f(x) =(|sinx|-|cosx|)/(|sin x + cosx|) i...

    Text Solution

    |

  14. The function f(x) = 3^(sin^(2)pi + sin^(4) pi x + x-[x]) where [x] den...

    Text Solution

    |

  15. Period of the function f(x) =(1)/(3){sin 3x + |sin 3x | + [sin 3x]} is...

    Text Solution

    |

  16. The function f(theta) = cos (pi sin^(2) theta), is

    Text Solution

    |

  17. Let f(x) = (1)/(sqrt(|x-1|-[x])) where[.] denotes the greatest intege...

    Text Solution

    |

  18. Let f(x)=[9^x-3^x+1] for all x in (-oo, 1), then the range of f(x) is,...

    Text Solution

    |

  19. If f(x) = log(e^2x) ((2lnx+2)/(-x)) and g(x) = {x} then range of g(x) ...

    Text Solution

    |

  20. f(x)=cos^(-1)sqrt(log([x])""abs(x)/x), where [*] denotes the greatest ...

    Text Solution

    |