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The question presented in the image is asking whether the solution set for the inequality \( x^2 + 1 \geq 0 \) is the empty set, denoted as \( \{ \} \).

### Let's analyze the inequality:

- The inequality is \( x^2 + 1 \geq 0 \).
- The term \( x^2 \) is the square of a real number, and the square of any real number is always non-negative (\( x^2 \geq 0 \)).
- Adding 1 to \( x^2 \) will always give a number greater than or equal to 1, since \( x^2 + 1 \geq 1 \).
  
Thus, the expression \( x^2 + 1 \) is always greater than or equal to 1 for all real numbers \( x \). Therefore, the inequality \( x^2 + 1 \geq 0 \) holds true for all real values of \( x \).

### Conclusion:
The solution set is not the empty set. In fact, the solution set is all real numbers, so the correct answer to the question should be **False** (since the solution set is not \( \{ \} \)).

Do you want more details or have any questions?

Here are five related questions:
1. What are the general properties of quadratic inequalities?
2. How do we solve an inequality of the form \( x^2 + c \geq 0 \) where \( c \) is a constant?
3. What does the empty set represent in the context of inequalities?
4. How would the inequality change if it were \( x^2 + 1 < 0 \)?
5. Can you think of any situation where the sum of a square and a constant could be negative?

**Tip:** Always check the behavior of the squared term in inequalities, as it can provide a lot of information about the solution set!

Himpunan penyelesaian pertidaksamaan x^2 + 1 ≥ 0 adalah {}.

Analyze the inequality x^2 + 1 ≥ 0 to understand its solution set. This problem involves key algebraic concepts, including inequalities and properties of quadratic equations. Suitable for students in Grades 9-11.

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