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The given function is \( f(x) = 4x - 5 \) with a domain \( x \in [1, 5] \), and we are asked to determine the range of this function.

### Step 1: Find the function values at the endpoints of the domain
- For \( x = 1 \):
  \[
  f(1) = 4(1) - 5 = 4 - 5 = -1
  \]
- For \( x = 5 \):
  \[
  f(5) = 4(5) - 5 = 20 - 5 = 15
  \]

### Step 2: The range of a linear function is between the minimum and maximum values of \( f(x) \) over the given domain. Since the function is increasing (positive slope), the minimum value is at \( x = 1 \) and the maximum value is at \( x = 5 \).

Thus, the range of the function is \( [-1, 15] \).

### Conclusion:
The correct answer is **A. [-1, 15]**.

Would you like further details or explanations? Here are 5 related questions to explore:

1. How do you find the range of a quadratic function?
2. What is the significance of the slope in determining the behavior of a linear function?
3. How do you solve for the inverse of a linear function?
4. Can the range of a linear function ever be a single point?
5. How would the range change if the domain was different?

**Tip:** The range of a function is highly dependent on the behavior (increasing or decreasing) and the domain of the function, especially for linear and polynomial functions.

Fungsi linier f(x) = 4x - 5 memiliki domain x ∈ [1,5]. Tentukan range dari fungsi tersebut.

Learn how to find the range of the linear function f(x) = 4x - 5, with the domain x ∈ [1, 5]. This problem covers key algebraic concepts for students in Grades 8-10.

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