Question

How do you find the inverse of `f(x) = (2x)/(3x-2)`?

Answer 1

`f(x)=\frac{2x}{3x-2}`

Explanation:

Given that

`f(x)={2x}/{3x-2}`

`3xf(x)-2f(x)=2x`

`(3f(x)-2)x=2f(x)`

`x=\frac{2f(x)}{3f(x)-2}`

Now, substituting `f(x)=x` & `x=f(x)` we get inverse function,

`f(x)=\frac{2x}{3x-2}`

Answer 2

`f^-1(x)=(2x)/(3x-2)`

Explanation:

`"let "y=(2x)/(3x-2)`

`"rearrange making x the subject"`

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

`3xy-2y=2x`

`3xy-2x=2y`

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

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

`rArrf^-1(x)=(2x)/(3x-2)`