AP EAMCET · Maths · Functions
The domain of the function \(y=f(x)\), where \(x\) and \(y\) are related by \(2^x+2^y=2\) is
- A \((-\infty, \infty)\)
- B \((-\infty, 1)\)
- C \((-1, \infty)\)
- D \((1, \infty)\)
Answer & Solution
Correct Answer
(B) \((-\infty, 1)\)
Step-by-step Solution
Detailed explanation
Given that \(2^x+2^y=2 \Rightarrow 2^y=2-2^x\) \[ \begin{aligned} & \because 2^y>0 \Rightarrow 2-2^x>0 \\ & \Rightarrow 2^x < 2 \Rightarrow x < 1 \Rightarrow x \in(-\infty, 1) \end{aligned} \]
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