1. ## Inverses

Is the inverse of $\displaystyle f(x)=ln|x|~if x<0$ if it's g lets say

$\displaystyle g(x)=e^{|x|}$??

if so is the domain all real numbers (for the inverse I mean)?

then the question says find a formula for computing $\displaystyle g(y)$ for each y in the domain of g

2. is $\displaystyle e^{|x|}$ some kind of parabola or something too?

3. Originally Posted by akhayoon
is $\displaystyle e^{|x|}$ some kind of parabola or something too?
Actually, yes it is because the negative side should mirror the positive side with f(0)=1.

4. Originally Posted by akhayoon
Is the inverse of $\displaystyle f(x)=ln|x|~if x<0$ if it's g lets say

$\displaystyle g(x)=e^{|x|}$??

if so is the domain all real numbers (for the inverse I mean)?

then the question says find a formula for computing $\displaystyle g(y)$ for each y in the domain of g
You already have the second part:
$\displaystyle g(y) = e^{|y|}$

Originally Posted by akhayoon
is $\displaystyle e^{|x|}$ some kind of parabola or something too?
It does look a bit "parabola-ish" doesn't it? (However it has little relation to an actual parabola.) We say that the function $\displaystyle g(x) = e^{|x|}$ has "even symmetry" when $\displaystyle g(-x) = g(x)$ as this one does.

-Dan

5. It does look a bit "parabola-ish" doesn't it? (However it has little relation to an actual parabola.) We say that the function has "even symmetry" when as this one does.
Yes, to be clear you shouldn't call it a parabola, but just state the fact that it is an even function. It probably doesn't matter unless you are in an Analysis class.

6. Originally Posted by akhayoon
Is the inverse of $\displaystyle f(x)=ln|x|~if x<0$ if it's g lets say

$\displaystyle g(x)=e^{|x|}$??

if so is the domain all real numbers (for the inverse I mean)?

then the question says find a formula for computing $\displaystyle g(y)$ for each y in the domain of g
The inverse of $\displaystyle y=ln|x|=ln(-x) (x<0)$ is $\displaystyle y=-e^x$.

7. As you can see, the inverse (like all functions that have inverses) is mirrored across the line y=x of the original function.