# Math Help - Need help on natural logs

1. ## Need help on natural logs

g(x) = ln sqrt (x+2)

Find the value of g^-1 (0)
How would I start? I'm stuck on this question for hours ! Please give me some hints. Thanks

2. Originally Posted by letzdiscuss
g(x) = ln sqrt (x+2)

Find the value of g^-1 (0)
How would I start? I'm stuck on this question for hours ! Please give me some hints. Thanks
Here's one way:

Let $y=g(x)=\ln\sqrt{x+2}$. To find the inverse, we swap x's and y's to get $x=\ln\sqrt{x+2}$. Now, we resolve the equation for y:

$x=\ln\sqrt{y+2}\implies e^x=\sqrt{y+2}\implies\dots\implies y=g^{-1}\left(x\right)=\dots$.

Then evaluate it at x=0.

Can you take it from here?

3. so to find the inverse you just switch the x and y and solve for y.

So if you have g(x) = y = ln sqrt (x+2)

you change it to x = ln sqrt (y+2) and solve for y:
x^e = sqrt(y+2)
x^2e = y+2

etc.

and if you want g inverse of 0, then you just plug in 0=x.

edit: woops, a minute too late. haha.

4. Originally Posted by letzdiscuss
g(x) = ln sqrt (x+2)

Find the value of g^-1 (0)
How would I start? I'm stuck on this question for hours ! Please give me some hints. Thanks
Start by letting $g(x)=y$ and then switching x and y. Then solve for y.

Ah! Beaten to the punch!

5. Thanks everyone !!!! That helped a lot !!
I really really appreciate it !

6. Originally Posted by letzdiscuss
g(x) = ln sqrt (x+2)

Find the value of g^-1 (0)
How would I start? I'm stuck on this question for hours ! Please give me some hints. Thanks
Or, since you are only asked for $g^{-1}(0)$, solve $0= ln(\sqrt{x+2}}$ for x. Taking the exponential of both sides, $e^0= 1= \sqrt{x+2}$. Squaring both sides, 1= x+2 so x= -1. That shows that g(-1)= 0 so $g^{-1}(0)= -1$.