Question

Find a counterexample: Let f(x) = x^2 + x - 10. Let y=f(x). Then y is always negative.

Will the counterexample just put in a value for x that allows y to be positive?

Answer 1

Yes. The statement is that: If x is a real number and y = x^2 + x - 10, then the value of y will be negative for all values of x.

Just find a value of x that makes the value of y positive.

Answer 2

okay. what about If f(x) = x^2 and g(x)=x^3 then f(x) is less than or equal to g(x) for all x that are elements of real numbers.

Answer 3

counterexample again.

Answer 4

Try x = 10. Run it through the function and look at the sign of the result. If the sign is positive, the x = 10 is a counterexample.

Answer 5

\[10^{2} \le 10^{3}\] so that proves it right....

Answer 6

let x=1/2