Question

Identify a counterexample to disprove −x ≤ x^2, where x is a real number.

options
a. x= -1/2
b. x = 0
c. x= 1/2
d. x= -2

Answer 1

a. x = -1/2

Explanation:

Replace x with each of the numbers in the choices in the given inequality until you find one that makes the inequality false.

Given inequality: -x ≤ x²

a. x = -1/2

-(-1/2) ≤ (-1/2)²

1/2 ≤ 1/4

False

Answer: a. x = -1/2