Let f:R → R and g:R → R be two functions defined by f(x) = log e (x² + 1) - e⁻ˣ + 1 and g(x) = (1 - 2e²ˣ)/(eˣ). Then, for which of the following range of α, the inequality f(g(((α - 1)²)/3)) > f(g(α -5/3)) holds ?

Sets, Relations and Functions: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jun, Morning shift · Q3828

JEE Main 202225 Jun, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let

f:R \to R

and

g:R \to R

be two functions defined by

f(x) = {\log _e}({x^2} + 1) - {e^{ - x}} + 1

and

g(x) = {{1 - 2{e^{2x}}} \over {{e^x}}}

. Then, for which of the following range of

\alpha

, the inequality

f\left( {g\left( {{{{{(\alpha - 1)}^2}} \over 3}} \right)} \right) > f\left( {g\left( {\alpha -{5 \over 3}} \right)} \right)

holds ?