Question

What is the inverse opperation of f (x)= x+2/3x-4

Answer 1

Given the function:
`f(x) = (x+2)/(3x-4)`

Step 1: Replace f(x) by y;

`y= (x+2)/(3x-4)`

Step 2: Interchange the variables x and y.

`x= (y+2)/(3y-4)`

Step 3: Solve for y in terms of x;

`x(3y-4) = y+2`

Using distributive property:
`a\cdot (b+c) = a\cdot b+ a\cdot c`

`3xy-4x = y+2`

Add 4x to both sides we get;

`3xy= y+2+4x`

`3xy-y=2+4x`

`y(3x-1)=2+4x`

⇒
`y = (4x+2)/(3x-1)`

Step 4: Replace y with
`f^(-1)(x)`

`f^(-1)(x) = (4x+2)/(3x-1)`

Therefore, the inverse operation of a given function is:

`f^(-1)(x) = (4x+2)/(3x-1)`