Class 12 Mathematics - Relations and Functions - Relations Medium Quiz

Mathematics Relations and Functions Relations Medium Class 12 Level 25

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Question 1/1 Medium Mathematics Relations and Functions Onto function Class 12 Level 25

यदि \(f:\mathbb{R}\to\mathbb{R}\), (f(x)=5x-11) है, तो (f) के आच्छादी होने के लिए किसी \(y\in\mathbb{R}\) का पूर्वप्रतिबिंब क्या होगा?

If \(f:\mathbb{R}\to\mathbb{R}\), (f(x)=5x-11), what will be the preimage of any \(y\in\mathbb{R}\) to show that (f) is onto?

Explanation opens after your attempt
Correct Answer

A. \(x=\frac{y+11}{5}\)

Step 1

Concept

To test onto nature, put (f(x)=y).

Step 2

Why this answer is correct

From (5x-11=y), we get \(x=\frac{y+11}{5}\), which is real for every real (y).

Step 3

Exam Tip

For a linear function, solving (x) in terms of (y) is the easiest method. चरण 1: आच्छादीपन जांचने के लिए (f(x)=y) रखें। चरण 2: (5x-11=y) से \(x=\frac{y+11}{5}\) मिलता है, जो हर वास्तविक (y) के लिए वास्तविक है। चरण 3: रैखिक फलन में (x) को (y) के रूप में निकालना सबसे सरल तरीका है।

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