Given below are two statements:

Statement-I: The function \(f:R\to R\) defined by \(f\left(x\right)=\frac{x}{1+\text{ }\left|x\right|}\) is one-one.

Statement-II: The function \(f:R\to R\) defined by \(f\left(x\right)=\frac{{x}^{2}+4x−30}{{x}^{2}−8x+18}\) is many-one.

In the light of the above statements, choose the correct answer from the options given below:

[JEE Main 2026, 28 Jan (Shift 2)]

Question

Given below are two statements:

Statement-I: The function \(f:R\to R\) defined by \(f\left(x\right)=\frac{x}{1+\text{ }\left|x\right|}\) is one-one.

Statement-II: The function \(f:R\to R\) defined by \(f\left(x\right)=\frac{{x}^{2}+4x−30}{{x}^{2}−8x+18}\) is many-one.

In the light of the above statements, choose the correct answer from the options given below:

[JEE Main 2026, 28 Jan (Shift 2)]

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Given below are two statements: Statement-I: The function \(f:R\to R\) defined by \(f\left(x\right)=\frac{x}{1+\text{ }\…