Question

Which is a counterexample that disproves the conjecture?

A student concludes that if x is a real number, then x ≤ x3.

A.
1

B.
0

C.
-1/2

D.
-2

Answer 1

A counter example is giving an example that disproves what was states
so we need to to disprove that for any x where x is a real number then \(x \leq x^3 \)
So lets find a value that is a real number buttttttt \(x>x^3\)
So lets just plug in a couple of points to figure this out
so lets x=1 then x^3=1 so 1=1 so that wont disprove it
Let x=2 then x^3=8 and 2<8 so this also does not disprove
How abt we take a negative number
Let x=-2 then x^3=-8 and -2>-8 SOOOO VOILAAA we have found a value of x that x>x^3 So this disproves the conjecture