# Can anyone help me find the natural domain and range of$$f(x) = • aek In summary, the conversation was about the importance of recycling and reducing waste. The speaker discussed how waste can harm the environment and gave tips on how to reduce waste, such as using reusable containers and avoiding single-use items. They also mentioned the benefits of composting and how to properly recycle different types of materials. Overall, the conversation emphasized the role of individuals in creating a more sustainable world through responsible waste management." aek can anyone help me find the natural domain and range of [tex]f(x) = 1 - log_3x$$
*the whole equation is under a square root sign, its just a couldn't latex it

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...

## 1. What is the natural domain of a function?

The natural domain of a function is the set of all possible input values (x-values) for which the function is defined. In other words, it is the set of values that can be plugged into the function to get a real number as the output.

## 2. How do I find the natural domain of a function?

To find the natural domain of a function, you need to look for any restrictions on the input values. This includes avoiding division by zero, taking the square root of a negative number, or any other operation that would result in an undefined or imaginary number. Once you have identified these restrictions, you can determine the set of valid input values.

## 3. What is the range of a function?

The range of a function is the set of all possible output values (y-values) that the function can produce. In other words, it is the set of values that the function can take on as its output for different input values.

## 4. How do I find the range of a function?

To find the range of a function, you can either graph the function and look at the y-values that are covered, or you can use algebraic methods. Algebraically, you can set up and solve equations to determine the possible output values for different input values. However, it is important to note that not all functions have a range that can be easily determined.

## 5. Can the natural domain and range of a function be the same?

Yes, it is possible for the natural domain and range of a function to be the same. This can happen when the function is defined for all real numbers and its output values cover all real numbers as well. In this case, the natural domain and range would both be the set of all real numbers, denoted as (-∞, ∞).

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