State the domain of these functions :
`f:xto5x`

Answer

To find the domain of the function \( f(x) = 5x \), we need to determine the set of all possible input values (x-values) for which the function is defined.

### Step-by-step Solution:

1. **Identify the function**: The function given is \( f(x) = 5x \).

2. **Understand the nature of the function**: This is a linear function, which means it is a straight line when graphed. Linear functions are defined for all real numbers.

3. **Determine the input values**: We need to check if there are any restrictions on the input values (x-values). In this case, there are no denominators, square roots, or logarithmic functions that would restrict the domain.

4. **State the domain**: Since there are no restrictions, the function is defined for all real numbers. Therefore, the domain of \( f(x) \) is all real numbers.

5. **Write the domain in interval notation**: The domain can be expressed in interval notation as \( (-\infty, \infty) \).

### Final Answer:
The domain of the function \( f(x) = 5x \) is all real numbers, which can be written as \( (-\infty, \infty) \).

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