# Given #f(x) = cosh(x+a/cosh(x+a/cosh( cdots)))# and #g(x)# its inverse, what is the minimum distance between then for #a > 0#?

Our goal is to find the shortest path between the function and

so then:

We need the derivative to vanish at a certain point in order for one of the two possible outcomes to occur:

If I have more time, I will go back to the solution.

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Assuming that y = g(x) ( in my view f(x) ) is the inverse, the distance is 0, everywhere.

Note on Disambiguation:

Writing a relation as y = f(x) is known as inversion.

Thus, if y equals f(x),

I believe it is past time to end the calling.

as the opposite.

The fact that the graphs for both are identical is significant.

This graph is rotated and altered by switching x and y.

Given that the two graphs are one and the distance is zero, I certify that

similar. For the shared graph, a = 1. It was necessary to define the inverse.

correspondingly.

Y = cosh(x+1/y) = the provided FCF (Functional Continued Function) graph

The expansion of a fraction f(x) is as follows: graph{(x - ln(y+(y^2-1)^0.5))(x + ln(y+(y^2-1)^0.5))=0}

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The minimum distance between f(x) and g(x) for a > 0 is 2a.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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