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General — Hard JEE math MCQ

Let the functions $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ be defined by \[ f(x)=e^{x-1}-e^{-|x-1|} \quad \text { and } \quad g(x)=\frac{1}{2}\left(e^{x-1}+e^{1-x}\right) \] Then the area of the region in the first quadrant bounded by the curves $y=f(x), y=g(x)$ and $x=0$ is
  1. A. $(2-\sqrt{3})+\frac{1}{2}\left(e-e^{-1}\right)$
  2. B. $(2+\sqrt{3})+\frac{1}{2}\left(e-e^{-1}\right)$
  3. C. $(2-\sqrt{3})+\frac{1}{2}\left(e+e^{-1}\right)$
  4. D. $(2+\sqrt{3})+\frac{1}{2}\left(e+e^{-1}\right)$

Solution

The correct option is **A**.

MATH

hard • PYQ Reworded
Question
Read carefully, then pick the best option.
Let the functions f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} and g:R→Rg: \mathbb{R} \rightarrow \mathbb{R} be defined by f(x)=ex−1−e−∣x−1∣ and g(x)=12(ex−1+e1−x) f(x)=e^{x-1}-e^{-|x-1|} \quad \text { and } \quad g(x)=\frac{1}{2}\left(e^{x-1}+e^{1-x}\right) Then the area of the region in the first quadrant bounded by the curves y=f(x),y=g(x)y=f(x), y=g(x) and x=0x=0 is
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