The given function f is one-to-one. Find f-1.

I can't seem to do the correct algebra to get the inverse. If someone could guide me a little, that would be wonderful. Thank you.

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- October 6th 2008, 04:04 PMtiarFinding the inverse of f(x)
The given function f is one-to-one. Find f-1.

I can't seem to do the correct algebra to get the inverse. If someone could guide me a little, that would be wonderful. Thank you. - October 6th 2008, 04:21 PMo_O
Let and change the x's and f(x)'s:

Simply solve for y. - October 6th 2008, 04:42 PMtiar
Thanks, I understand that part. Afterwards, however, do I move the squareroot to the x? I tried...

So is that the inverse (incomplete answer)? I don't believe that's right. i'm just not getting something in the algebra. ugh.. - October 6th 2008, 05:01 PMo_O
You're just solving for y in terms of x:

There's only one step left to do ... - October 6th 2008, 06:16 PMtiar

??

Then turn it into...

??

Is that it? Things are always much simpler than they seem, lol. Thank you! - October 6th 2008, 06:25 PM11rdc11
- October 6th 2008, 06:25 PMo_O
You copied incorrectly.

However, note that the range of f(x) was . Since we interchanged x's and y's, the**domain**of is - October 6th 2008, 06:34 PMtiar
Thanks both of you. It was illogical of me to move the "y" over when it could have been isolated right away. At least I see that now.

I have a question in regards to range. You are saying it is because in the original equation, , we cannot have a negative under the square root thus it must be greater than zero. How do you know that this is your range and not domain? The domain would be , correct? Wait, did I just answer my own question? I just need clarification.

- October 6th 2008, 06:45 PM11rdc11
When finding inverses just switch the domain and range.

So if f(x) domain is A and f(x) range is B then domain is B and range A

Does this make sense? - October 6th 2008, 07:06 PMtiar
Yes, that makes perfect sense, thanks.