#### To determine

**To find:** Find the inverse function f-1.

#### Answer

The inverse function is f-1x=ex/2+1

#### Explanation

**Calculation**: y=2ln(x-1)

To find the inverse function f-1, we first write the function as y=2ln(x-1)

Now, we solve this equation for x

y2=ln(x-1)

Apply the exponential function on both sides

ey/2=(x-1)

ey/2+1=x

We interchange x and y:

y=ex/2+1

Therefore, the inverse function is

f-1(x)=ex/2+1

**Final statement:** The inverse function is f-1x=ex/2+1