JEE Mains · Maths · STD 12 - 1. relation and function
Given below are two statements:
Statement I: The function \(f:R\rightarrow R\) defined by \(f(x)=\frac{x}{1+|x|}\) is one-one.
Statement II: The function \(f:R\rightarrow R\) defined by \(f(x)=\frac{x^{2}+4x-30}{x^{2}-8x+18}\) is many-one.
In the light of the above statements, choose the correct answer from the options given below :
- A Both Statement I and Statement II are false.
- B Both Statement I and Statement II are true.
- C Statement I is false but Statement II is true.
- D Statement I is true but Statement II is false.
Answer & Solution
Correct Answer
(B) Both Statement I and Statement II are true.
Step-by-step Solution
Detailed explanation
Statement 1: \(f(x)=\frac{x}{1+|x|}\) \(f(x)=\begin{cases}\frac{x}{1+x}&x\ge0\\ \frac{x}{1-x}&x<0\end{cases}\) \(f(x)\) is one-one Statement 2: \(f(x)=\frac{x^2+4 x-30}{x^2-8 x+18}, f(0)=\frac{-30}{18}=\frac{-5}{3}\) \(\frac{-5}{3}=\frac{x^{2}+4x-30}{x^{2}-8x+18}\) On solving…
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