JEE Mains · Maths · STD 12 - 1. relation and function
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 many-one in \((1, \infty)\)
- C \(f(x)\) is one-one in \([1, \infty)\) but not in \((-\infty, \infty)\)
- D \(f ( x )\) is one-one in \((-\infty, \infty)\)
Answer & Solution
Correct Answer
(C) \(f(x)\) is one-one in \([1, \infty)\) but not in \((-\infty, \infty)\)
Step-by-step Solution
Detailed explanation
\(f(x)=\frac{(x+1)^2}{x^2+1}=1+\frac{2 x}{x^2+1}\) \(f(x)=1+\frac{2}{x+\frac{1}{x}}\)
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