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GATE 2023 EE – Question 7

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Which one of the following options represents the given graph?

Diagram for GATE 2023 EE question 7
  1. $f(x)=x^22^{-|x|}$
  2. $f(x)=x\,2^{-|x|}$
  3. $f(x)=|x|\,2^{-x}$
  4. $f(x)=x\,2^{-x}$

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Show answer and explanation

Correct answer: (B) $f(x)=x\,2^{-|x|}$

Explanation

The curve is odd (negative on the left, positive on the right, zero at the origin) and decays to zero on both sides. $x\,2^{-|x|}$ is odd and decays, so it fits. $x^22^{-|x|}$ is even, $|x|2^{-x}$ blows up for $x<0$, and $x2^{-x}$ also blows up on the left.