Let ƒ : R → R and g : R → R be two functions defined by ƒ(x) = log e (x 2 + 1) – e –x + 1 and g(x) = x x 2 e e 2 1 − . Then, for which of the following range of α , the inequality ƒ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 5 − α ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − α 3 g ƒ 3 ) 1 ( g 2 holds ?

Question

Let ƒ : R → R and g : R → R be two functions defined by ƒ(x) = log e (x 2 + 1) – e –x + 1 and g(x) = x x 2 e e 2 1 − . Then, for which of the following range of α , the inequality ƒ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 5 − α > ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − α 3 g ƒ 3 ) 1 ( g 2 holds ?

Accepted Answer

(2, 3)

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