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.
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.
Substitute y for f(x)
so y= 2/(x-3)
Interchange the variables x and y
Raise both sides to the negative 1 power
Multiply both sides by 2
Add 3 to both sides
2/x + 3 = y
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.