Finding the Inverse of a Function

The problem reads find the inverse of f(x)= 2/y-3

I have the solutions manual and it says to multiply both sides by y-3 to clear the fraction. However, I find this to be too much work. I prefer to take both sides to the -1 power. Is this okay? I get the same answer which is f^-1(x)= 2/x + 3.

I just find the other method to be too much work and this method to be easier, faster and cleaner.

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Originally Posted by petergunz

The problem reads find the inverse of f(x)= 2/y-3

I have the solutions manual and it says to multiply both sides by y-3 to clear the fraction. However, I find this to be too much work. I prefer to take both sides to the -1 power. Is this okay? I get the same answer which is f^-1(x)= 2/x + 3.

I just find the other method to be too much work and this method to be easier, faster and cleaner.

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There is often more than one correct approach to a problem. Use the approach you feel most comfortable with.

By the way, if y - 3 is the denominator of your expression you should write it as f(x) = 2/(y - 3) to avoid confusion. Ditto your answer.

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Originally Posted by mr fantastic

There is often more than one correct approach to a problem. Use the approach you feel most comfortable with.

By the way, if y - 3 is the denominator of your expression you should write it as f(x) = 2/(y - 3) to avoid confusion. Ditto your answer.

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You are only referring to this message board right? Seeing as how my text does not say this.

I know that there is more than one way, my question is whether multiplying to the negative inverse of one was acceptable mathematically. I believe this to be so, but I have not been told this, so I was wondering if anyone with more experience knows.

In any case, thanks for the reply. For a minute it looked like no one was going to reply.

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Originally Posted by petergunz

You are only referring to this message board right?

Mr F says: Yes.

Seeing as how my text does not say this.

I know that there is more than one way, my question is whether multiplying to the negative inverse of one was acceptable mathematically. I believe this to be so, but I have not been told this, so I was wondering if anyone with more experience knows.

Mr F says: What you have said you've done sounds OK. But perhaps you should post the details of your calculation just so there's no misunderstanding.

In any case, thanks for the reply. For a minute it looked like no one was going to reply.

Mr F says: When were you expecting to get a reply? About 6 hours or so has elapsed between when you posted and when I replied. I don't see why a wait of 6 hours should cause you to worry that no-one was going to reply.

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Originally Posted by mr fantastic

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f(x)= 2/(x-3) (sorry I typed it wrong the first time)
Substitute y for f(x)
so y= 2/(x-3)
Interchange the variables x and y
x= 2/(y-3)
Raise both sides to the negative 1 power
1/x= (y-3)/2
Multiply both sides by 2
2/x= y-3
Add 3 to both sides
2/x + 3 = y
Final Answer
f^-1(x)= 2/x + 3

I noticed that on the forum if the question does not get answered within a short time frame (like a few hours) generally they do not get answered. See my post on word problems in the Misc section to see what I mean. Also, there was another question on this board that had the same problem. I am aware of the policies so I know that there is a chance that my question will not be answered, I was just saying that I'm glad. that mine did.