Problem

We are given the curves

y=\int_{-\infty}^{x} f(t)\,dt

through the point

\left(0,\frac{1}{2}\right)

and

y=f(x)

, where

f(x)>0

and

f(x)

is differentiable,

\forall x\in\mathbb{R}

, through

(0,1)

. If tangents drawn to both the curves at the points with equal abscissae intersect at the same point on the

X

-axis, then the number of solutions of

f(x)=2e^x

is equal to a. 0 b. 1 c. 2 d. None of these