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We are given two functions:
- \( g(x) = 4x + 3 \)
- \( f(x) = \frac{2x + 7}{x + 1} \)

The question asks us to determine the value of \( x \) for which \( f(x) \) is undefined.

### Solution:
For \( f(x) \) to be undefined, the denominator must be equal to zero, since division by zero is not allowed.

The denominator of \( f(x) \) is \( x + 1 \). We need to find when this expression equals zero:
\[
x + 1 = 0
\]
Solving for \( x \):
\[
x = -1
\]

Therefore, \( f(x) \) is undefined when \( x = -1 \).

Would you like further details or have any questions?

### Additional Questions:
1. How do you determine when a rational function is undefined?
2. Can you explain how to find the domain of \( f(x) \)?
3. What happens to the graph of \( f(x) \) at \( x = -1 \)?
4. How do you solve equations like \( x + 1 = 0 \)?
5. Can the function \( g(x) = 4x + 3 \) ever be undefined?

**Tip:** Always check the denominator of rational functions to ensure you're not dividing by zero when determining the domain.

State the value of x for which f(x) is undefined given the function f(x) = (2x + 7) / (x + 1).

This math problem involves finding the value of x for which the function f(x) = (2x + 7)/(x + 1) is undefined. Explore key concepts like rational expressions and the conditions for undefined points. Suitable for students in Grades 8-10.

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