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If \(f(x)=\frac{x+2}{x-2}\) and \(g(x)=\frac{x-2}{x+2}\), what is the domain of \(\left(\frac{f}{g}\right)(x)\)?यदि \(f(x)=\frac{x+2}{x-2}\) और \(g(x)=\frac{x-2}{x+2}\) हैं, तो \(\left(\frac{f}{g}\right)(x)\) का प्रांत क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\mathbb{R}\setminus{-2,2}\)\(\mathbb{R}\setminus{-2,2}\)
In \(\frac{f}{g}\), both (f) and (g) must be defined and (g(x)\ne 0); this excludes \(x=\pm2\). In a quotient, zero of the second function is also forbidden.\(\frac{f}{g}\) में (f) और (g) दोनों परिभाषित हों और (g(x)\ne 0); इससे \(x=\pm2\) हटते हैं। भागफल में दूसरे फलन का शून्य भी निषिद्ध होता है।
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