iven below are two statements : Statement I : The function defined by is one-one. Statement II : The function defined by is many-one. In the light of the above statements, choose the correct answer from the options given below :

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Solution

Q.
Given below are two statements :

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

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

In the light of the above statements, choose the correct answer from the options given below : [2026]

1 Both Statement I and Statement II are false

2 Statement I is true but Statement II is false

3 Statement I is false but Statement II is true

4 Both Statement I and Statement II are true

Ans.
(4)

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