# What is the inverse function of #f(x) = cosh(x+a/cosh(x+a/cosh(x+cdots)))# with domain and range?

##### 2 Answers

#### Explanation:

I confine myself to FCF-naming of the function. For me, the strain is

inevitable.

For this FCF,

The operand is clear in the cosh function, in contrast to either f(x)

or

Inversely,

the inverse of

= the inverse of the equivalent

Now, the inverse is

For a = 1, I use here the inverse for the FCF y = cosh(x+1/y) as

graph that reveals domain and range.

Indeed, x admits negative values.

The graphs for y = f(x) and its inverse

the same.

As any cosh value

The domain/range:

Graph of y = cosh(x + 1/y):

Note that there is no axis of symmetry.

The lowest point (-1, 1) is plotted in the graph.

graph{(x-ln(y+(y^2-1)^0.5)+1/y)(x+ln(y+(y^2-1)^0.5)+1/y)((x+1)^2+(y-1)^2-.004)=0 [-5 5 -1 4]}

Combined graph below, for this and y = cosh x reveals the

patterns.

This graph is my present to those (Caserio, George et al) who had

shown keen interest in FCF.

graph{(x-ln(y+(y^2-1)^0.5)+1/y)(x+ln(y+(y^2-1)^0.5)+1/y)(x-ln(y+(y^2-1)^0.5))(x+ln(y+(y^2-1)^0.5))=0[-5 5 0 10]}

.

#### Explanation:

From

Finally

then