0 reads0 ratings0 helpful
Find the domain of the function \(f(x)=\dfrac{\sqrt{x-1}}{x-5}\).फलन \(f(x)=\dfrac{\sqrt{x-1}}{x-5}\) का परिभाषा-क्षेत्र (domain) ज्ञात कीजिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \([1,5)\cup(5,\infty)\)\([1,5)\cup(5,\infty)\)
For \(f(x)=\dfrac{\sqrt{x-1}}{x-5}\), two conditions:
1) Square root: \(x-1\ge 0\Rightarrow x\ge 1\).
2) Denominator not zero: \(x-5\neq 0\Rightarrow x\neq 5\).
Combine: \(x\in[1,\infty)\) but excluding \(x=5\). Hence domain is \([1,5)\cup(5,\infty)\).\(f(x)=\dfrac{\sqrt{x-1}}{x-5}\) के लिए दो शर्तें:
1) वर्गमूल के लिए: \(x-1\ge 0\Rightarrow x\ge 1\).
2) हर शून्य नहीं होना चाहिए: \(x-5\neq 0\Rightarrow x\neq 5\).
दोनों मिलाकर: \(x\in[1,\infty)\) है लेकिन \(x=5\) को निकालना होगा। अतः domain \([1,5)\cup(5,\infty)\) है।
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.
