f(x)=-2ln(x+1)

Find the domain of f.

So, far this is I have:

f(x)=-2ln(x+1)

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

Can anyone go over this problem step by step with me?

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- Apr 6th 2008, 06:47 PMwickwikiDomain Logarithmic Function (Solved)
f(x)=-2ln(x+1)

Find the domain of f.

So, far this is I have:

f(x)=-2ln(x+1)

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

Can anyone go over this problem step by step with me? - Apr 6th 2008, 06:53 PMMathstud28Ok to find the domain
for $\displaystyle f(x)=-2\ln(x+1)$...the only problem is that $\displaystyle x+1\geq{0}$ due to $\displaystyle \ln(x)$s properties...so $\displaystyle x+1\geq{0},x\geq{-1}$

- Apr 6th 2008, 06:55 PMTheEmptySet
The domain of

$\displaystyle g(x)=\ln(x)$

is the set $\displaystyle (0,\infty)$

so your function is related to the unshifted natrual log by

$\displaystyle f(x)=-2g(x+1)=-2\ln(x+1)$ This shifts the graph one unit left in the x direction so the domain is

$\displaystyle (-1,\infty)$ - Apr 6th 2008, 06:56 PMJhevon
- Apr 6th 2008, 07:03 PMMathstud28O man
I had it that way...but I was thinking of $\displaystyle \sqrt{x}$ and I went back and changed it...on these forums I try to answer as fast as I can so I get messed up sometimes...thanks!...I knew that by the way =D

- Apr 6th 2008, 07:13 PMJhevon
- Apr 6th 2008, 07:15 PMMathstud28Haha
::blushes:: haha thanks

- Apr 6th 2008, 07:24 PMwickwiki
OK, solution solved thanks for the help.

I would like to know a bit more about how you solved it.

f(x)=-2ln(x+1)

So, what happens with the negative two exactly?

Because the one of my similar problems I solved ln(x+4) and I got

Domain= (-4,\infty).

So, how is the -2 effect the equation? - Apr 6th 2008, 07:27 PMMathstud28It doesnt
The only thing that matters in a $\displaystyle \ln(u(x))$ is that the domain is restricted so that $\displaystyle \forall{x}\in{Domain},u(x)>0$...make sense?