GATE 2023 CY – Question 7

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

Which one of the following options represents the given graph?

$f(x)=x^2 2^{-|x|}$
$f(x)=x2^{-|x|}$
$f(x)=|x|2^{-x}$
$f(x)=x2^{-x}$

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Correct answer: (A) $f(x)=x^2 2^{-|x|}$

Explanation

The curve is symmetric about the vertical axis, vanishes at 0 and decays towards zero in both tails. The function x²2^(−|x|) satisfies all three conditions, so **A**. Option B changes sign with x, while C and D fail the left-tail decay or symmetry test.