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If \(f(x)=x+\frac{2}{x}\) and \(g(x)=x-\frac{2}{x}\), what is ((fg)(x)) equal to?यदि \(f(x)=x+\frac{2}{x}\) और \(g(x)=x-\frac{2}{x}\) हैं, तो ((fg)(x)) किसके बराबर है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x^2-\frac{4}{x^2}\), (x\ne 0)\(x^2-\frac{4}{x^2}\), (x\ne 0)
\((fg)(x)=\left(x+\frac{2}{x}\right)\left(x-\frac{2}{x}\right)=x^2-\frac{4}{x^2}\). Apply \((a+b)(a-b)=a^2-b^2\).\((fg)(x)=\left(x+\frac{2}{x}\right)\left(x-\frac{2}{x}\right)=x^2-\frac{4}{x^2}\)। पहचान \((a+b)(a-b)=a^2-b^2\) लगाएं।
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