The number of real solutions of the equation ` 1+|e^x - 1|= e^x (e^x - 2) ` is :

Options

A. 1
B. 2
C. 4
D. 8

Answer

To solve the equation \( 1 + |e^x - 1| = e^x (e^x - 2) \), we will follow these steps:

### Step 1: Substitute \( e^x \) with \( t \)
Let \( t = e^x \). The equation now becomes:
\[ 1 + |t - 1| = t(t - 2) \]