Can anyone help me find the natural domain and range of[tex]f(x) =

AI Thread Summary
The function f(x) = √(1 - log₃x) requires that the argument of the square root is non-negative, leading to the condition 1 - log₃x ≥ 0. This implies that log₃x must be less than or equal to 1, which translates to x ≤ 3. Additionally, log₃x is defined for x > 0, establishing the natural domain as (0, 3]. The range is determined by the values of f(x), which will vary from 0 to 1 as x approaches 3. Thus, the natural domain is (0, 3] and the range is [0, 1].
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can anyone help me find the natural domain and range of

f(x) = 1 - log_3x
*the whole equation is under a square root sign, its just a couldn't latex it
 
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so it's f(x) = \sqrt{1 - \log_3{x}}?

Well, when is \log_3{x} defined? When is \sqrt{x} defined?
 
Two suggestions to build off of Data's. \log_3{x} = \frac{\ln{x}}{\ln3}

and

1 - \log_{3}x \geq 0
 
Accidently doubled posted...
 
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