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If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=\frac{x^2-4}{x-2}), why is the claim that it is a function on all of (\mathbb{R}) false?यदि (f:\mathbb{R}\to\mathbb{R}) और (f(x)=\frac{x^2-4}{x-2}) हो, तो दावा कि यह पूरे (\mathbb{R}) पर फलन है, क्यों गलत है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because the formula is undefined at (x=2)क्योंकि (x=2) पर सूत्र अपरिभाषित है
Even though simplification looks like (x+2), the original formula is undefined at (x=2). When deciding domain, check the original denominator.भले सरलीकरण (x+2) जैसा दिखे, मूल सूत्र (x=2) पर परिभाषित नहीं है। प्रांत तय करते समय मूल हर को देखें।
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