Question

Determine whether the statement is true or false. If X1 < x2 and f is a decreasing function, then f(x1) > f(x2).

a) True
b) False

Answer 1

The statement is a) true. If X1 < X2 and f is a decreasing function, then f(X1) > f(X2).

Step-by-step explanation:

The statement is true.

If X₁ < X₂ and f is a decreasing function, then f(X₁) > f(X₂).

This is because when X₁ is less than X₂, it means that the input value X₁ is closer to the left side of the x-axis compared to X₂.

Since f is a decreasing function, it means that as the input value decreases, the output value of the function increases.

For example, if X₁ = 3 and X₂ = 5, and f(X) = 2X, then f(X₁) = 2(3) = 6 and f(X₂) = 2(5) = 10.

Therefore, f(X₁) = 6 is greater than f(X₂) = 10.