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For the function defined by \(f(x)=\frac{1}{|x+1|-3}\), what is its largest possible real domain?\(f(x)=\frac{1}{|x+1|-3}\) द्वारा परिभाषित फलन का अधिकतम वास्तविक प्रांत क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\mathbb{R}\setminus\{-4,2\}\)\(\mathbb{R}\setminus\{-4,2\}\)
The denominator must not be zero. Solving \(|x+1|-3=0\) gives \(|x+1|=3\), so \(x=2\) or \(x=-4\). These are the only excluded values, and the domain is therefore \(\mathbb{R}\setminus\{-4,2\}\).हर शून्य नहीं होना चाहिए। \(|x+1|-3=0\) हल करने पर \(|x+1|=3\) मिलता है, इसलिए \(x=2\) या \(x=-4\)। यही दो मान वर्जित हैं; अतः प्रांत \(\mathbb{R}\setminus\{-4,2\}\) है।
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