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)=\frac{1-2 e^{2 x}}{e^x}. Then, for which of the following range of \alpha, the inequality f(g(\frac{(\alpha-1)^2}{3}))>f(g(\alpha-\frac{5}{3})) holds ? [25-Jun-2022-Shift-1]

JEE Main 25 June 2022 Shift 1 Solved Paper

Section: Mathematics

Question : 13 of 90

Marks: +1, -0

Let f:R→R and g:R→R be two functions defined by f(x)=loge(x2+1)−e−x+1 and g(x)=‌

1−2e2x

. Then, for which of the following range of α, the inequality f(g(‌

(α−1)2

))>f(g(α−‌

)) holds ?

[25-Jun-2022-Shift-1]

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