Math Is Fun Forum

student007

Member

Registered: 2005-12-13

Posts: 2

Need help with finding inverse of function

Find inverse of this function
F(X) = X/3X-2

Interchange X & Y
Y = X/3X-2
X = Y/3Y-2
X(3Y-2) = Y
3XY-2X = Y

I'm not sure what to do from here any help would be appreciated. Thanks

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Need help with finding inverse of function

x(3y - 2) = y
x = y / (3y - 2)

---

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

student007

Member

Registered: 2005-12-13

Posts: 2

Re: Need help with finding inverse of function

thank you

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Need help with finding inverse of function

Whoops, you used a different way of finding the inverse than I'm used to, so I got mixed up.

What I normally do is:

y = x/(3x - 2)
y(3x - 2) = x
3xy - 2y = x
3xy - x = 2y
x(3y - 1) = 2y
x = 2y / (3y - 1)

What you did was pretty much the same, but you switched the x and y variables, as it is standard to want to solve for y:

x = y/(3y - 2)
x(3y - 2) = y
3xy - 2x = y
3xy - y = 2x
y(3x - 1) = 2x
y = 2x / (3x-1)

As you can see, you come up with the same answer, just different names for the variables.  In mine, x is dependant on y, in yours (as it normally is), y is dependant on x.

---

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."