jee-main 2023 Q77

jee-main · India · session1_25jan_shift1 Stationary points and optimisation Determine intervals of increase/decrease or monotonicity conditions

Let $f : ( 0,1 ) \rightarrow \mathbb { R }$ be a function defined by $f ( x ) = \frac { 1 } { 1 - e ^ { - x } }$, 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,
(1) Only (I) is true
(2) Only (II) is true
(3) Neither (I) nor (II) is true
(4) Both (I) and (II) are true

Let $f : ( 0,1 ) \rightarrow \mathbb { R }$ be a function defined by $f ( x ) = \frac { 1 } { 1 - e ^ { - x } }$, 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,\\
(1) Only (I) is true\\
(2) Only (II) is true\\
(3) Neither (I) nor (II) is true\\
(4) Both (I) and (II) are true

Paper Questions

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