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If \(f(x)=\frac{x-2}{x+2}\) and \(g(x)=\frac{x+2}{x-2}\), what is \(\left(\frac{f}{g}\right)(x)\) equal to?यदि \(f(x)=\frac{x-2}{x+2}\) और \(g(x)=\frac{x+2}{x-2}\) हैं, तो \(\left(\frac{f}{g}\right)(x)\) किसके बराबर है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\frac{(x-2)^2}{(x+2)^2},\ x\ne\pm2\)\(\frac{(x-2)^2}{(x+2)^2},\ x\ne\pm2\)
\(\frac{f}{g}=\frac{x-2}{x+2}\cdot\frac{x-2}{x+2}=\frac{(x-2)^2}{(x+2)^2}\). The restrictions \(x\ne\pm2\) from the original functions remain.\(\frac{f}{g}=\frac{x-2}{x+2}\cdot\frac{x-2}{x+2}=\frac{(x-2)^2}{(x+2)^2}\)। दोनों मूल फलनों के प्रतिबंध \(x\ne\pm2\) रहेंगे।
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