Question

If f and g are continuous at x_0, max{f,g} and min{f,g} are continuous at x_0.

A. True
B. False

Answer 1

If f and g are continuous at x_0, max{f,g} and min{f,g} are also continuous at x_0. the statement is true

Step-by-step explanation:

In this case, the statement is true. If f and g are continuous at x₀, then max{f,g} and min{f,g} are also continuous at x₀.

To understand why this is true, recall that the maximum function takes two values and returns the larger value, while the minimum function takes two values and returns the smaller value. Since f and g are continuous at x₀, we can evaluate them at x₀, and the result will be continuous as well.

For example, consider the functions h(x) = max{sin(x), cos(x)} and j(x) = min{sin(x), cos(x)}. Both sin(x) and cos(x) are continuous functions, so h(x) and j(x) are also continuous.