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Inverse of g(x)= ln(2x+12)?

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1. I have no idea :/
I'm using MyMaths doing questions from it, but it doesn't help you when you're stuck, so I'm left not knowing what to do.

Inverse of g(x)=ln(2x+12)
2. (Original post by JaredzzC)
I have no idea :/
I'm using MyMaths doing questions from it, but it doesn't help you when you're stuck, so I'm left not knowing what to do.

Inverse of g(x)=ln(2x+12)
Given y, how do you find out what x is? (A formula for x, if you like)

Eg with a simpler example, if y = lnx, what's the inverse of that?
3. (Original post by SeanFM)
Given y, how do you find out what x is? (A formula for x, if you like)

Eg with a simpler example, if y = lnx, what's the inverse of that?
I know that the inverse of y = lnx is y=e^x and if I were to use an example of:

y = e^x-2 then invese of y = ln(x-2)
because y-2=e^x therefore ln(x-2)=x
but my brain can't translate the other question.
4. (Original post by JaredzzC)
I know that the inverse of y = lnx is y=e^x and if I were to use an example of:

y = e^x-2 then invese of y = ln(x-2)
because y-2=e^x therefore ln(x-2)=x
but my brain can't translate the other question.
I think you swapped a 3 for a 2 there but no worries.

So you have y = ln(2x+12), so the first step is to try and isolate the 2x+12.. how can you do that?
5. (Original post by SeanFM)
I think you swapped a 3 for a 2 there but no worries.

So you have y = ln(2x+12), so the first step is to try and isolate the 2x+12.. how can you do that?
Yea, sorry :P Getting late and not as concentrated as I should be.

Get the inverse of it? I think I've done it...

I did e^y=e^[ln(2x+12)]
e=2x+12
x=(e-12)/2
x=(1/2)e^x - 6 ???
6. (Original post by JaredzzC)
Yea, sorry :P Getting late and not as concentrated as I should be.

Get the inverse of it? I think I've done it...

I did e^y=e^[ln(2x+12)]
e=2x+12
x=(e-12)/2
x=(1/2) - 6 ???
Pretty close. Don't let the e^y disappear though. And you've turned e/2 into 1/2 somehow but that should be 0.5e^y - 6, then you're fine. (maybe swap the y and x with x and f^-1(x) respectively as well)
7. This is how I see it:

g(x) can be assumed to be y so y = ln(2x+12)

All you now have to do is solve for x and then you get your inverse.

So it's,
y = ln(2x+12)
e^y = 2x+12
2x = (e^y)-12
x = ((e^y)-12)/2
g^-1(x) = (e^y)/2 - 6
8. (Original post by SeanFM)
Pretty close. Don't let the e^y disappear though. And you've turned e/2 into 1/2 somehow but that should be 0.5e^y - 6, then you're fine. (maybe swap the y and x with x and f^-1(x) respectively as well)
Thanks Sean and Ash : )

Yea, I'm confusing myself a bit too much and muddling things up.

I was using MyMaths and it accepeted 1/2 :/ I guess I may be confusing myself again. I know that e = 2.718...., so e/2 can't be 0.5, is it an error on the websites part or (most likely) an error from my understanding of it and my rearrangement?

https://gyazo.com/b9835dc854ba25decd41c5e0810df100
9. (Original post by JaredzzC)
Thanks Sean and Ash : )

Yea, I'm confusing myself a bit too much and muddling things up.

I was using MyMaths and it accepeted 1/2 :/ I guess I may be confusing myself again. I know that e = 2.718...., so e/2 can't be 0.5, is it an error on the websites part or (most likely) an error from my understanding of it and my rearrangement?

https://gyazo.com/b9835dc854ba25decd41c5e0810df100
e/2 is not involved at all, and only appeared because you did the entire process wrong.
Simply:
g(x) = ln(2x+12) -> e^g(x) = 2x + 12 -> x = (e^g(x) -12)/2 = 1/2*e^g(x)-6,
so g^-1(x) = 1/2*e^x - 6.

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