Let $f : (0, \infty) \to R$ be a (strictly) decreasing function. If $f (2 a^{2} + a + 1) < f (3 a^{2} - 4 a + 1),$ then the range of $a \in R$ is

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Solution

Given $f$ is decreasing function
$f (2 a^{2} + a + 1) < f (3 a^{2} - 4 a + 1) ⟹ 2 a^{2} + a + 1 > 3 a^{2} - 4 a + 1 ⟹ a^{2} - 5 a < 0 ⟹ a \in (0, 5)$

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