Inverses

**akhayoon** · December 9th 2007, 07:10 AM

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

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

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

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

**akhayoon** · December 9th 2007, 03:28 PM

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

**colby2152** · December 9th 2007, 04:49 PM

Originally Posted by akhayoon

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

Actually, yes it is because the negative side should mirror the positive side with f(0)=1.

**topsquark** · December 9th 2007, 05:46 PM

Originally Posted by akhayoon

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

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

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

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

You already have the second part:
$g(y) = e^{|y|}$

Originally Posted by akhayoon

is $e^{|x|}$ 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 $g(x) = e^{|x|}$ has "even symmetry" when $g(-x) = g(x)$ as this one does.

-Dan

**colby2152** · December 9th 2007, 06:35 PM

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.

**curvature** · December 9th 2007, 09:40 PM

Originally Posted by akhayoon

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

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

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

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