Question

Which value of x provides a counter example to the assertion that x > 1/x for all x ≥ 1 ?

x =

Answer 1

The value x = 1 is a counterexample to the assertion that x > 1/x for all x ≥ 1, as it results in the equality 1 = 1, disproving the original inequality.

Step-by-step explanation:

The question asks for a counterexample to the assertion that x > 1/x for all x ≥ 1. To find a value of x that disproves this assertion, we can set x equal to 1, which is the smallest value x can have in the given range. At x = 1, the inequality x > 1/x becomes 1 > 1/1, which simplifies to 1 > 1. This is clearly not true, as 1 equals 1, not greater than 1. Therefore, the value of x = 1 serves as a counterexample to the statement, showing that the inequality does not hold for all values of x greater than or equal to 1.