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GATE 2023 EC – 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 EC 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: (A) $f(x)=x^22^{-|x|}$

Explanation

The curve is positive on both sides, zero at $x=0$, symmetric about the $y$-axis and decays to 0 for large $|x|$. $x^22^{-|x|}$ is even, non-negative and decays, so it fits. $x2^{-|x|}$ is odd (negative for $x<0$), $|x|2^{-x}$ grows without bound for $x<0$, and $x2^{-x}$ is neither even nor decaying on the left.