Question

An increasing function satisfies ______ and ______. Which of the following statements about the inverse of the function must be true.

Answer 1

An increasing function satisfies two properties: as the input increases, the output also increases, and as the input decreases, the output also decreases. If a function has an inverse, it means that the roles of the input and output are reversed. So, if the original function is increasing, its inverse will be decreasing; and if the original function is decreasing, its inverse will be increasing. Therefore, if a function is increasing, its inverse must be decreasing.

Step-by-step explanation:

An increasing function satisfies two properties: as the input increases, the output also increases, and as the input decreases, the output also decreases.

If a function has an inverse, it means that the roles of the input and output are reversed. So, if the original function is increasing, its inverse will be decreasing; and if the original function is decreasing, its inverse will be increasing.

Therefore, if a function is increasing, its inverse must be decreasing.