Inverse functions

[wondering]

Decide whether the function has an inverse function. If so, what is the inverse function?

1) h(t) is the height of the tide t hours after midnight, where \(\displaystyle 0 \leq x < 24 \)

I said that the function is not monotonic, so it can't have an inverse. I was thinking that the height must always be positive and high tide happens twice in a 24 hour period.

This is in the inverse section of a Calculus book. (begining of Calc 2)
Thoughts. Is this the correct reasoning?

 

[Deleted member 4993]

Decide whether the function has an inverse function. If so, what is the inverse function?

1) h(t) is the height of the tide t hours after midnight, where \(\displaystyle 0 \leq x < 24 \)

I said that the function is not monotonic, so it can't have an inverse. I was thinking that the height must always be positive and high tide happens twice in a 24 hour period.

This is in the inverse section of a Calculus book. (begining of Calc 2)
Thoughts. Is this the correct reasoning?

You are correct.

Another way to say that would be that the function would have failed horizontal line test, within the given domain.

 

[mmm4444bot]

I was thinking that the height must always be positive

This is not always the case; there are differing systems of measurement for tides.

What matters about the question of an inverse function is that tide functions oscillate (i.e., they are not monotonic, as you realized). This is the key to realizing that they have no inverse function. (You do not need to consider the sign of the function values.)

Good job. :cool: