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]`
Doubtnut Promotions Banner Mobile Dark
|

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

Knowledge Check

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

    A
    `{y:yle0}`
    B
    `{y:yge-9}`
    C
    `{y:yle9}`
    D
    `{y:yge0}`

    • Similar Questions

    Explore conceptually related problems

    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

    Home
    Profile