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If (f(x)=\frac{1}{x^2+1}) and (g(x)=x^2+1), on which domain is (fg) the constant function (1)?यदि (f(x)=\frac{1}{x^2+1}) और (g(x)=x^2+1) हैं, तो (fg) किस डोमेन पर स्थिर फलन (1) है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ( \mathbb{R} )( \mathbb{R} )
Since (x^2+1>0) for every real (x), both (f) and (g) are defined on all (\mathbb{R}). Hence (fg=1) on all (\mathbb{R}).क्योंकि (x^2+1>0) हर वास्तविक (x) के लिए है, (f) और (g) दोनों पूरे (\mathbb{R}) पर परिभाषित हैं। अतः (fg=1) पूरे (\mathbb{R}) पर है।
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