The equation of the tangent to the curve f(x) = 1 + e–2x where it cuts the line y = 2 is

x + 2y = 2 2x + y = 2 x – 2y = 1 x – 2y + 2 = 0

2x + y = 2

When y = 2,  e–2x = 1 ⇒ x = 0, and $\frac{df}{dx} = -2e^{-2x} ⇒ \frac{df}{dx}|_{x=0} = - 2$ ⇒ The equation of the tangent is, (y - 2) = - 2 (x - 0) ⇒ 2 x + y - 2 = 0. Hence (B) is the correct answer.