Question

Let \( f(x) = x^2 + 6x + 1 \) and let \( R \) denote the set of points \( (x, y) \) in the coordinate plane such that \( f(x) + f(y) \) so and \( f(x) - f(y) \leq 0 \). Which of the following is closest to the area of \( R \)?

• A. 22
• B. 23
• C. 24
• D. 25

Hint:

In inequalities involving quadratic functions, you can complete the square to make the analysis easier and find the area of the region.

Answer 1

The Correct Option is D

The area of the region \( R \) can be found by solving the inequality \( f(x) + f(y) \leq 0 \) and \( f(x) - f(y) \leq 0 \). The closest value to the area is \( 25 \).