Functions Question 8
Question 8 - 29 January - Shift 1
Let $f: R \to R$ be a function such that $f(x)=\frac{x^{2}+2 x+1}{x^{2}+1}$. Then
(1) $f(x)$ is many-one in $(-\infty,-1)$
(2) $f(x)$ is many-one in $(1, \infty)$
(3) $f(x)$ is one-one in $[1, \infty)$ but not in $(-\infty, \infty)$
(4) $f(x)$ is one-one in $(-\infty, \infty)$
Show Answer
Answer: (3)
Solution:
Formula: Graph of function, Many one function, One-one function, Operations on functions
$f(x)=\frac{(x+1)^{2}}{x^{2}+1}=1+\frac{2 x}{x^{2}+1}$
$f(x)=1+\frac{2}{x+\frac{1}{x}}$
