GATE 2023 CS – Question 9

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

$f(x)$ and $g(y)$ are functions of $x$ and $y$, respectively, and $f(x) = g(y)$ for all real values of $x$ and $y$. Which one of the following options is necessarily TRUE for all $x$ and $y$?

$f(x)=0$ and $g(y)=0$
$f(x)=g(y)=\text{constant}$
$f(x)\neq \text{constant}$ and $g(y)\neq \text{constant}$
$f(x)+g(y)=f(x)-g(y)$

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Correct answer: (B) $f(x)=g(y)=\text{constant}$

Explanation

Since x and y vary independently, the left side cannot depend on x and the right side cannot depend on y. So both must equal the same constant.