What is the inverse of ln(x^2) and its symmetry properties?

[ludi_srbin]

f(x)=e^cosx

equation for the axis of symmetry?
I got x=pi


f(x)=ln(x^2 - 20)

describe symmetry??

I got symmetric arround y axis.

inverse??

I got y=sqr of ((x/ln) +20)

f(x)=ln(x^2)

Inverse?

I got y= sqr of (x/ln)

 

[Diane_]

Since cos x is a repeating function, it has an infinite number of axes of symmetry. They occur at n pi. Something similar needs to be done for exp(cos x).

For the others, you seem to be using "ln" as a variable of some sort. Remember that ln x is a function, with inverse exp(x). You might want to look at those again.

 

[ludi_srbin]

So for others I just change ln to exp?

 

[ludi_srbin]

So I get f(x)^-1=e^(X^2-20)

and

f(x)^-1=e^x^2

 

[Diane_]

Let me take one of them. You should be able to do the rest.

y = ln(x^2 - 20)

exp(y) = x^2 - 20

x^2 = exp(y) + 20

x = sqrt(exp(y) + 20)

So, f^-1(x) = sqrt(exp(x) + 20)

Note that there are restrictions on the domain and range - these would correspond to the restrictions on the range and domain of the original function.

Does that help?

 

[ludi_srbin]

It does.

Thank you so much.