Class 12 Mathematics - Relations and Functions - Relations Expert Quiz

Mathematics Relations and Functions Relations Expert Class 12 Level 23

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Question 1/1 Expert Mathematics Relations and Functions One-one function Class 12 Level 23

यदि \(f:\mathbb{R}\to\mathbb{R}\) को (f(x)=x-3-3x) से परिभाषित किया गया है, तो यह फलन किस अंतराल पर एकैकी है?

If \(f:\mathbb{R}\to\mathbb{R}\) is defined by (f(x)=x-3-3x), on which interval is the function one-one?

Explanation opens after your attempt
Correct Answer

A. \((-\infty,-1]\) पर एकैकीOne-one on (\(-\infty,-1]\)

Step 1

Concept

Check monotonic behaviour to test one-one nature.

Step 2

Why this answer is correct

(f'(x)=3x-2-3=3(x-1)(x+1)), so the function is increasing on (\(-\infty,-1]\).

Step 3

Exam Tip

In exams, the sign of the derivative is the quickest method for such cubic functions. चरण 1: एकैकी जांचने के लिए बढ़ने-घटने का व्यवहार देखें। चरण 2: (f'(x)=3x-2-3=3(x-1)(x+1)), इसलिए (\(-\infty,-1]\) पर फलन लगातार बढ़ता है। चरण 3: परीक्षा में ऐसे घन फलनों के लिए अवकलज का संकेत सबसे तेज तरीका है।

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