Question

Find the inverse of f(x)=(3x)/(x-2)

Answer 1

So here are the steps to finding an inverse of a function:

1. Change f(x) to y
2. Switch the positions of x and y
3. Solve for y
4. Change y to f^1(x)

Firstly, apply the first two steps:

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

Now, let's solve for y. Firstly, multiply both sides by y-2:

$x(y-2)=3y\\xy-2x=3y$

Next, subtract xy on both sides:

$-2x=3y-xy$

Next, factor out y on the right side of the equation:

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

Lastly, divide both sides by 3 - x:

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

Now, apply the last step and your final answer will be $-\frac{2x}{3-x}=f^{-1}(x)$