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If the domain of the function \(f(x)=|x+2|\) is \([1,5]\), what is its range?यदि फलन \(f(x)=|x+2|\) का डोमेन \([1,5]\) है, तो इसका रेंज क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \([3,7]\)\([3,7]\)
For every \(x\in[1,5]\), \(x+2\) is positive, so \(f(x)=x+2\). This function increases on the domain: its minimum is \(f(1)=3\), and its maximum is \(f(5)=7\). Therefore, the range is \([3,7]\).\([1,5]\) के प्रत्येक \(x\) के लिए \(x+2\) धनात्मक है, इसलिए \(f(x)=x+2\)। यह फलन डोमेन पर बढ़ता है: इसका न्यूनतम मान \(f(1)=3\) और अधिकतम मान \(f(5)=7\) है। इसलिए इसका रेंज \([3,7]\) है।
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