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) constant and g(y) constant

GATE CSE 2023 Q9: f(x) ≡ g(y) for all real x and y

General Aptitude
2 marks
MCQ
−2/3 if wrong

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

Try it: multiple choice: exactly one correct option

Wrong answer costs 2/3 mark in GATE.

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Answer: B (official GATE 2023 final answer key)

Concept used: A function of $x$ alone that equals a function of $y$ alone for all $x, y$ must be constant.

First step: Fix $y$ and vary $x$ : $f(x)$ equals the same number $g(y)$ for every $x$ .

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Source: official GATE 2023 CS question paper and final answer key, organised by IIT Kanpur. Question paper · Answer key

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GATE CSE 2023 Q9: f(x) ≡ g(y) for all real x and y

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