Question

Find the inverse of (x)/(x-2)

Answer 1

umm it says the answer is (2x)/(x-1) so you're wrong

Answer 2

f(x) = x/(x-2) Looking at this we know that x cannot equal 2 because then the bottom would be 0.
Let's change f(x) to y just to make it more simple to manipulate the equation.
y= x/(x-2)
Now multiply the other side to have a common denominator
y(x-2) = x
Multiply it out
yx - 2y = x
Put all the x's on one side and every thing else on the other side
yx - x = 2y
Keep manipulating the equation
x ( y - 1 ) = 2y
Now just solve for x
x = 2y/ (y - 1)
And for the final step just reverse the variables x for y and vice versa.

y = 2x/(x-1)

Do you understand what I did?

Answer 3

yes and it is very nice too.

Answer 4

Thank you :)

Answer 5

thanks that was really helpful

Answer 6

now that you are a pro, try this
\[f(x)=\frac{x}{x-2}\]
\[y=\frac{x}{x-2}\]
\[y(x-2)=x\] etc

Answer 7

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