**Inverse function f‐¹ of f(X)=2x**

To find the inverse function f‐¹ of f(X)=2x, we need to determine the function that will "undo" the original function by reversing its operations. In other words, we want to find a function that, when applied to the output of f(X)=2x, will give us back the original input.

**Step 1: Replace f(X) with y**

Let's start by replacing f(X) with y in the original function:

y = 2x

**Step 2: Swap the variables**

To find the inverse function, we need to swap the variables x and y. This means that wherever we have x, we replace it with y, and wherever we have y, we replace it with x:

x = 2y

**Step 3: Solve for y**

Now, we solve the equation for y to find the inverse function:

Divide both sides of the equation by 2:

x/2 = y

Therefore, the inverse function is:

f‐¹(x) = x/2

**Explanation:**

The inverse function f‐¹ of f(X)=2x is given by f‐¹(x) = x/2. This means that if we take a value of x, apply the function f(X)=2x to it, and then apply the inverse function f‐¹(x) to the result, we will get back the original value of x.

For example, let's say we have x = 4. If we apply the function f(X)=2x to it, we get f(4) = 2(4) = 8. Now, if we apply the inverse function f‐¹(x) to 8, we get f‐¹(8) = 8/2 = 4, which is the original value of x.

Similarly, if we take any value of x, apply the function f(X)=2x to it, and then apply the inverse function f‐¹(x) to the result, we will always get back the original value of x. This is the property of inverse functions.

Therefore, the inverse function f‐¹(x) = x/2 undoes the original function f(X)=2x by dividing the input x by 2.