If (f:\mathbb{R}\setminus{-1}\to\mathbb{R}) is defined by (f(x)=\frac{x-1}{x+1}), choose the correct statement about (f).

Correct answer: It is one-one

Step 1: To check one-one nature, assume (f(a)=f(b)). Step 2: From (\frac{a-1}{a+1}=\frac{b-1}{b+1}), we get ((a-1)(b+1)=(b-1)(a+1)); simplifying gives (2a=2b), so (a=b). Step 3: In rational functions, remember to exclude the value that makes the denominator zero.