Question

Let $f: R \rightarrow R$ be a function such that $f(x)=\frac{x^2+2 x+1}{x^2+1}$. Then

• A. $f(x)$ is many-one in $(-\infty,-1)$
• B. $f(x)$ is one-one in $(-\infty, \infty)$
• C. $f(x)$ is many-one in $(1, \infty)$
• D. $f(x)$ is one-one in $[1, \infty)$ but not in $(-\infty, \infty)$

Answer 1

Answer: (D)

$ f(x)=\frac{(x+1)^2}{x^2+1}=1+\frac{2 x}{x^2+1} $
$ f(x)=1+\frac{2}{x+\frac{1}{x}}$