Find the domain of f (x) =x/4 +1

(-0,-4) (-4,0∞)

(-0,4) U (4,00)

(-∞, 0) U (0,0).
(18,8)

To find the domain of the function \( f(x) = \frac{x}{4} + 1 \), we need to determine the set of all possible values of \( x \) for which the function is defined.

### Analysis of the Function
The function \( f(x) = \frac{x}{4} + 1 \) is a linear function. Linear functions are defined for all real numbers since there are no restrictions like division by zero or square roots of negative numbers.

### Domain
The domain of \( f(x) = \frac{x}{4} + 1 \) is therefore all real numbers, which is typically represented as \( (-\infty, \infty) \).

### Provided Options:
Let's analyze the options given:

1. **Option 1**: \((-0,-4) (-4,0∞)\) - This is not a valid representation and seems to be a mistake.
2. **Option 2**: \((-0,4) \cup (4,\infty)\) - This represents two intervals excluding the values \( x = 0 \) and \( x = 4 \), which is incorrect because the function is defined for all \( x \).
3. **Option 3**: \((-∞, 0) \cup (0,0)\) - This option is incorrect because the domain excludes \( x = 0 \) and does not cover all real numbers.
4. **Option 4**: \((18,8)\) - This option is not correct, as it suggests a single interval from 18 to 8, which is also written incorrectly (should be \( (8,18) \)).
   
None of these options correctly describe the domain of the function.

### Correct Domain:
The correct domain is:

\[
\text{Domain: } (-\infty, \infty)
\]

Would you like more details, or do you have any other questions?

**Related Questions:**
1. What is the domain of \( f(x) = \frac{1}{x - 2} \)?
2. How do you find the domain of \( f(x) = \sqrt{x + 5} \)?
3. What is the effect of adding a constant to a function on its domain?
4. How do you determine the domain of a function with a square root and a fraction?
5. Can a linear function ever have a restricted domain?

**Tip:** The domain of a linear function \( f(x) = ax + b \) is always all real numbers, \( (-\infty, \infty) \), unless explicitly restricted by the problem context.

Discover how to determine the domain of the function f(x) = x/4 + 1. This linear function analysis covers its domain, which extends over all real numbers due to its linear nature. Suitable for high school students studying functions and algebra.

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