AP EAMCET · Maths · Functions
The solution set contained in \(R\) of the inequation \(3^x+3^{1-x}-4 < 0\), is :
- A \((1,3)\)
- B \((0,1)\)
- C \((1,2)\)
- D \((0,2)\)
Answer & Solution
Correct Answer
(B) \((0,1)\)
Step-by-step Solution
Detailed explanation
We have, \(3^x+3^{1-x}-4 < 0\) \(3^x+\frac{3}{3^x}-4 < 0\) \(3^{2 x}+3-4 \cdot 3^x < 0\) \(3^{2 x}-4 \cdot 3^x+3 < 0\) \(\left(3^x-1\right)\left(3^x-3\right) < 0\) \(1 < 3^x < 3 \Rightarrow 0 < x < 1\) \(\therefore \quad\) The solution set is \((0,1)\).
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