Question

Determine whether the statement below is true or false. A function is increasing on an open interval I if, for any choice of x1 and x2 in I, with x1 < x2 we have f(x1) > f(x2).

Answer 1

Answer: False.

Step-by-step explanation:

This says;

If we have an interval I, f(x) is increasing if, for any two x1, x2 such that:

x1 ∈ I and x2 ∈ I.

where x2 > x1, ----> f(x1) > f(x2).

An increasing function means that, if the value of x increases, also does the value of f(x).

Particularly, here we have that x2 > x1

so x can increase from x1 to x2.

But we have that f(x1) > f(x2)

So here we can see that the actual value of f(x) decreases as x increases.

Then this is not a increasing function, so the statement is false.