Chapter 1.9, Problem 102E

To determine

Determine whether the given situation can be represented by one to one function ,also write a statement that best describes the inverse function.

Answer to Problem 102E

The given situation is periodic function and no periodic function is one-to-one also function $d\left(t\right)$ cannot have an inverse function.

Explanation of Solution

Given:

The depth of the tide $d$ at a beach in terms of the time $t$ over a 24-hour period.

A function can have an inverse only if the function is one-to-one and onto in nature.

Now, in this case, the function $d\left(t\right)$ is oscillatory or periodic in nature.

An oscillatory or periodic function $f\left(x\right)$ gives multiple values as output for different values of the input $x$ , repeated after a certain interval T.

Hence, no periodic function is one-to-one.

Hence the function $d\left(t\right)$ cannot have an inverse function.