Let f:(0,1) be a function defined f(x) = 1/(1 - e⁻ˣ), and g(x) = (f(- x) - f(x)). Consider two statements (I) g is an increasing function in (0, 1) (II) g is one-one in (0, 1) Then,

(B) Neither (I) nor (II) is true

Limit, Continuity and Differentiability: JEE Main 2023 Mathematics question

JEE Main 2023 · 25 Jan, Morning shift · Q2728

JEE Main 202325 Jan, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f:(0,1)\to\mathbb{R}

be a function defined

f(x) = {1 \over {1 - {e^{ - x}}}}

, and

g(x) = \left( {f( - x) - f(x)} \right)

. Consider two statements (I) g is an increasing function in (0, 1) (II) g is one-one in (0, 1) Then,

JEE Main 2023 · 25 Jan, Morning shift · Q2728

JEE Main 202325 Jan, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f:(0,1)\to\mathbb{R}

be a function defined

f(x) = {1 \over {1 - {e^{ - x}}}}

, and

g(x) = \left( {f( - x) - f(x)} \right)

. Consider two statements (I) g is an increasing function in (0, 1) (II) g is one-one in (0, 1) Then,