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Functions question

2022 · 25 Jun · Shift 1 · Q33

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JEE Main
Mathematics
Functions
2022 · 25 Jun · Shift 1 · Q33

Functions question

2022 · 25 Jun · Shift 1 · Q33

JEE MainMathematicsFunctionsMCQ+4 / −1

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) \gt f\left( {g\left( {\alpha -{5 \over 3}} \right)} \right)

holds ?

A
(2, 3)
B
( $-$ 2, $-$ 1)
C
(1, 2)
D
( $-$ 1, 1)

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