SOLUTION: If f(x)= 2/(x-1), then f^-1(x)= ? The way I tried solving this problem is by switching the x and y, and solving for y. I ended up with the answer f^-1(x)=(2+x)/x. Can you help m

Algebra ->  Inverses -> SOLUTION: If f(x)= 2/(x-1), then f^-1(x)= ? The way I tried solving this problem is by switching the x and y, and solving for y. I ended up with the answer f^-1(x)=(2+x)/x. Can you help m      Log On


   

Question 623825: If f(x)= 2/(x-1), then f^-1(x)= ?
The way I tried solving this problem is by switching the x and y, and solving for y. I ended up with the answer f^-1(x)=(2+x)/x. Can you help me decide if this is the right answer, and let me know where I went wrong if this answer is wrong.
Found 2 solutions by edjones, lwsshak3:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)= 2/(x-1)
y=2/(x-1)
x=2/(y-1)
y-1=2/x
y=(2/x) + 1
f^-1(x)= (2/x) + 1
.
Ed

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
If f(x)= 2/(x-1), then f^-1(x)=
**
Find the inverse:
y=2/(x-1)
switch x and y like you did, then solve for y
x=2/y-1
xy-x=2
xy=2+x
y=(2+x)/x
f^-1=(2+x)/x
your answer is correct