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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]`
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