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The image shows a function and a request to find its domain. The given function is:

\[
f(x) = \frac{5}{2x + 2}
\]

### Step-by-Step Solution:

1. **Domain**: 
   To find the domain, we need to determine where the denominator \(2x + 2\) is non-zero, because division by zero is undefined.

   Set the denominator equal to zero:
   \[
   2x + 2 = 0
   \]
   Solving for \(x\):
   \[
   2x = -2 \quad \Rightarrow \quad x = -1
   \]

   Therefore, the function is undefined at \(x = -1\). The domain of the function is all real numbers except \(x = -1\).

   So, the domain of \(f(x)\) is:
   \[
   \boxed{(-\infty, -1) \cup (-1, \infty)}
   \]

2. **Range**: 
   The function \(f(x) = \frac{5}{2x+2}\) is a rational function. Since the numerator is constant (\(5\)) and the denominator can take any real value except 0, the range is also affected by the values of the function. As \(x\) approaches infinity or negative infinity, \(f(x)\) approaches 0 but never reaches it.

   Thus, the range is all real values except \(y = 0\):
   \[
   \boxed{(-\infty, 0) \cup (0, \infty)}
   \]

Would you like more details or have any questions?

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Here are some related questions:

1. How do you determine the domain of more complex rational functions?
2. What happens to the range if the numerator of a rational function is a variable?
3. Can you explain horizontal and vertical asymptotes in this context?
4. How would you find the inverse of this function?
5. What would the graph of this function look like?

**Tip**: When finding the domain of rational functions, always check for values that make the denominator zero.

Find the domain and range of the function f(x) = 5 / (2x + 2).

This problem explores how to find the domain and range of the rational function f(x) = 5 / (2x + 2). Learn how to determine where the function is undefined and the range of values it can take. This solution is suitable for students in Grades 9-11.

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