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)

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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).