Given below are two statements: Statement I: The function f: R → R defined by f(x) = x/(1+|x|) is one-one. Statement II: The function f: R → R defined by f(x) = (x²+4x-30)/(x²-8x+18) is many-one. In the light of the above statements, choose the correct answer from the options given below:

(B) Both Statement I and Statement II are true

(A) Statement I is false but Statement II is true

(C) Both Statement I and Statement II are false

(D) Statement I is true but Statement II is false

Sets, Relations and Functions: JEE Main 2026 Mathematics question

JEE Main 2026 · 28 Jan, Evening shift · Q2

JEE Main 202628 Jan, Evening shiftMathematicsMediumSets, Relations and Functions168× since 2002

Given below are two statements : Statement I : The function

f: \mathbb{R} \to \mathbb{R}

defined by

f(x) = \frac{x}{1+|x|}

is one-one. Statement II : The function

f: \mathbb{R} \to \mathbb{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 :

JEE Main 2026 · 28 Jan, Evening shift · Q2

JEE Main 202628 Jan, Evening shiftMathematicsMediumSets, Relations and Functions168× since 2002

Given below are two statements : Statement I : The function

f: \mathbb{R} \to \mathbb{R}

defined by

f(x) = \frac{x}{1+|x|}

is one-one. Statement II : The function

f: \mathbb{R} \to \mathbb{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 :