Question

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

Answer 1

Answer:

Given the function: $f(x) = \frac{x+2}{3x-4}$

Step 1: Replace f(x) by y;

$y= \frac{x+2}{3x-4}$

Step 2:  Interchange the variables x and y.

$x= \frac{y+2}{3y-4}$

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;

$3xy= y+2+4x$

$3xy-y=2+4x$

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

⇒$y = \frac{4x+2}{3x-1}$

Step 4: Replace y with $f^{-1}(x)$

$f^{-1}(x) = \frac{4x+2}{3x-1}$

Therefore, the inverse operation of a given function is:

$f^{-1}(x) = \frac{4x+2}{3x-1}$