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If \(f(x)=\frac{1}{x-1}\) and \(g(x)=x+3\), what is the domain of \(\left(\frac{g}{f}\right)(x)\)?यदि \(f(x)=\frac{1}{x-1}\) और \(g(x)=x+3\) हैं, तो \(\left(\frac{g}{f}\right)(x)\) का प्रांत क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x \in \mathbb{R}, x \neq 1\)\(x \in \mathbb{R}, x \neq 1\)
(f(x)) needs \(x \neq 1\), and \(f(x)=\frac{1}{x-1}\) is never zero. So the only restriction is \(x \neq 1\).(f(x)) के लिए \(x \neq 1\) चाहिए और \(f(x)=\frac{1}{x-1}\) कभी शून्य नहीं होता। इसलिए केवल \(x \neq 1\) प्रतिबंध है।
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