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Many-One onto Function

If 3 x + 2...

Question

If $3^{x + 2} - 9^{- 1 / x} > 0$ then find interval of $x .$

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Solution

$3^{(x + 2)} > 3^{(- 2 / x)}$
$\Rightarrow x + 2 > \frac{- 2}{x}$
$\Rightarrow x^{2} + 2 x + 2 > 0$
${(x + 1)}^{2} + 1 > 0$
(always true)
So, $x \in R$

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Many-One onto Function

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