Maths Olympiad Prep

Track / Stage 4 / 222 of 340 #482 of 1964

Problem 482

AMC 12 late, AIME early
Algebra Difficulty 4.9 Find the answer

(7) Given the sets P={y∣y=x2+3x+1,x∈R},Q={y∣y=−x2−3x+1P=\left\{y \mid y=x^{2}+3 x+1, x \in \mathbf{R}\right\}, Q=\left\{y \mid y=-x^{2}-3 x+1\right., x∈R}x \in \mathbf{R}\}, find P∩QP \cap Q.

A number or a short expression. Spacing, $ signs and \frac vs / are all fine.

Official solution

 (7) P∩Q=[−54,134]\begin{array}{l}\text { (7) } P \cap Q= \\ {\left[-\frac{5}{4}, \frac{13}{4}\right]}\end{array}

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.