Find the inverse of 2/2x-1 and verify.

Answer 1

y = 2/(2x-1)
2x-1 = 2/y
2x = 1 + 2/y
x = 1/2 + 1/y
so, the inverse is 1/2 + 1/x = (x+2)/2x

Answer 2

and the verification?

Answer 3

I kinda figure you would take care of that yourself...

you want f(f^-1(x)) = x

so, plug in (x+2)/2x into the original equation and make sure you wind up with just x.

2/(2[(x+2)/2x]-1)
= 2/((x+2)/x - 1)
= 2/((x+2-x)/x)
= 2/(2/x)
= 2*x/2
= x