0 reads0 ratings0 helpful
Which is the correct classification of the function \(h:\mathbb{R}\to\mathbb{R}\), where \(h(x)=x^3+x\)?फलन \(h:\mathbb{R}\to\mathbb{R}\), जहाँ \(h(x)=x^3+x\), का सही वर्गीकरण कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: One-one and ontoएक-एक तथा आच्छादक
For \(a>b\), both \(a^3>b^3\) and \(a>b\), so \(a^3+a>b^3+b\); hence the function is one-one. As this cubic takes values from \(-\infty\) to \(+\infty\), it is onto \(\mathbb{R}\) too. Exam tip: always check the codomain.\(a>b\) होने पर \(a^3>b^3\) और \(a>b\), इसलिए \(a^3+a>b^3+b\); अतः फलन एक-एक है। घन बहुपद के मान \(-\infty\) से \(+\infty\) तक जाते हैं, इसलिए यह आच्छादक भी है। परीक्षा टिप: डोमेन और सह-डोमेन अवश्य जाँचें।
Student feedback
Was this question useful?
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Difficulty
Easy0%
Medium0%
Hard0%
Was the explanation clear?
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
