# What is the inverse function for f(x) = x / (x - 2)?

**Solutions :**

Given:

Function f(x) = x / (x - 2)

Now we have to find the inverse of the given function.

**Step 1 :**

Substitute function is equal to y.

f(x) = y

⇒ y = x / (x - 2)

**Step 2 :**

Now interchange x with y

⇒ x = y / (y - 2)

**Step 3 :**

Now solve the equation for y

⇒ x = y / (y - 2)

⇒ x (y - 2) = y

⇒ xy - 2x = y

⇒ xy - y = 2x

⇒ y(x - 1) = 2x

⇒ y = 2x / (x - 1)

Now, because we interchanged x with y

y = f^{-1}(x) (inverse of the function)

f^{-1}(x) = 2x / (x - 1)

**Therefore, the inverse of the function f(x) = x / (x - 2) is f ^{-1}(x) = 2x / (x - 1).**

## What is the inverse function for f(x) = x / (x - 2)?

**Summary:**

The inverse of the function f(x) = x / (x - 2) is f⁻¹(x) = 2x / (x - 1).