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Question 397870: I did the following problem, but I am not certain I did it correctly. I am hoping a tutor can double check this for me, and put me on the right path if it is wrong. Any help would be greatly appreciated! Here is the problem:
Find f^-1(x)
f(x)= (2x-3)/(x+1)
Here's how I did it:
f(x)=2x-3/(x+1)
y=2x-3/(x+1)
x=(2y-3)/(y+1)
xy= (2y-3)/(y+1)*y
xy= 2y-3
xy-2y=-3
y(x-2)/(x-2)=-3/(x-2)
y=-3/(x-2)
so f^-1(x)= -3/(x-2)
Ok...Is this correct, or do I need to go back to the drawing board? Could someone please show me how to check these? Thank you!
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! I did the following problem, but I am not certain I did it correctly. I am hoping a tutor can double check this for me, and put me on the right path if it is wrong. Any help would be greatly appreciated! Here is the problem:
Find f^-1(x)
f(x)= (2x-3)/(x+1)
Here's how I did it:
f(x)=2x-3/(x+1)
y=2x-3/(x+1)
x=(2y-3)/(y+1)
xy= (2y-3)/(y+1)*y
xy= 2y-3 ****** That won't work.
xy-2y=-3
y(x-2)/(x-2)=-3/(x-2)
y=-3/(x-2)
so f^-1(x)= -3/(x-2)
Ok...Is this correct, or do I need to go back to the drawing board? Could someone please show me how to check these? Thank you!
-----------------
x=(2y-3)/(y+1)
x(y+1) = 2y-3
xy+x = 2y-3
xy - 2y = -x-3
y(x-2) = -x-3
y = (-x-3)/(x-2)
y = -(x+3)/(x-2)
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