The solution set contained in $R$ of the inequation $3^{x} + 3^{1 - x} - 4 < 0$ is

(1, 3)

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(0, 1)

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(1, 2)

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(0, 2)

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Solution

The correct option is D $(0, 1)$
$3^{x} + \frac{1}{3^{x}} - 4 < 0$
Let $3^{x} = t$
$(t^{2} - 4 t + 3) < 0$
$(t - 1) (t - 3) < 0$
$(3^{x} - 1) (3^{x} - 3) < 0$
$1 < 3^{x} < 3$
$0 < x < 1$

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