Let's analyze the function [tex]\( f(x) = \frac{1}{5} \)[/tex].
### Step-by-Step Solution
1. Understanding the Function:
- The function [tex]\( f(x) = \frac{1}{5} \)[/tex] is a constant function. This means that, for any value of [tex]\( x \)[/tex], the function will always return the same constant value, which is [tex]\( \frac{1}{5} \)[/tex] or 0.2.
2. Finding the Domain:
- The domain of a function is the set of all possible input values (x-values) for which the function is defined.
- Since [tex]\( f(x) \)[/tex] is a constant function and does not depend on [tex]\( x \)[/tex], it can accept any real number as input.
- Therefore, the domain of [tex]\( f(x) \)[/tex] is all real numbers.
3. Finding the Range:
- The range of a function is the set of all possible output values (y-values).
- For [tex]\( f(x) = \frac{1}{5} \)[/tex], the output is always the constant value [tex]\( \frac{1}{5} \)[/tex] regardless of the input [tex]\( x \)[/tex].
- Thus, the range of [tex]\( f(x) \)[/tex] is just the single value [tex]\( \frac{1}{5} \)[/tex], which is greater than zero.
4. Conclusion:
- The domain of [tex]\( f(x) = \frac{1}{5} \)[/tex] is all real numbers.
- The range of [tex]\( f(x) = \frac{1}{5} \)[/tex] is the single value [tex]\( \frac{1}{5} \)[/tex], which is indeed greater than zero.
Based on this analysis:
- The domain is all real numbers.
- The range is all real numbers greater than zero.
So the correct description is:
The domain is all real numbers. The range is all real numbers greater than zero.
