# What is the inverse of the function f(x) = (2x +1)/x?

**Solution:**

Given:

Function f(x) = (2x +1) / x

As we know that f(x) = y

Therefore,

x = f ^{-1}(y)

Given, f(x) = (2x +1) /x

y = (2x +1) /x

**Step 1: **Multiply both sides by x.

⇒ xy = 2x + 1

**Step 2: **Subtract both sides by 2x.

⇒xy - 2x = 1

**Step 3: **Take out the common terms.

⇒ x(y - 2) = 1

**Step 4: **Divide both the sides by (y - 2).

⇒ x = 1 / (y - 2)

We know that x = f^{-1}(y)

## What is the inverse of the function f(x) = (2x +1) / x?

**Summary:**

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