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GUJCET · Maths · Relations and Functions
If \(f(x)=\frac{1+x}{1-x} ; x \neq 1\), then, \(f(x) \cdot f(y)=\) ____________ .
- A \(f\left(\frac{x+y}{1-x y}\right)\)
- B \(f\left(\frac{x+y}{1+x y}\right)\)
- C \(f(x) \cdot f(y)\)
- D \(f\left(\frac{1}{1+x y}\right)\)
Answer & Solution
Correct Answer
(B) \(f\left(\frac{x+y}{1+x y}\right)\)
Step-by-step Solution
Detailed explanation
\(f(x) \cdot f(y) = \frac{1+x}{1-x} \cdot \frac{1+y}{1-y}\) \( = \frac{(1+x)(1+y)}{(1-x)(1-y)} = \frac{1+x+y+xy}{1-x-y+xy}\)
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