MHT CET · Maths · Functions
The domain of definition of the function \(y(x)\) is given by the equation \(2^x+2^y=2\), is
- A \(0 \lt x \leq 1\)
- B \(0 \leq x \leq 1\)
- C \(-\infty \lt x \leq 0\)
- D \(-\infty \lt x \lt 1\)
Answer & Solution
Correct Answer
(D) \(-\infty \lt x \lt 1\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & 2^x+2^y=2 \\ & \Rightarrow 2^y=2-2^x \\ & \Rightarrow y=\log _2\left(2-2^x\right) \text { is defined, if } 2-2^x\gt0 \\ & \Rightarrow 2^x \lt 2 \\ & \Rightarrow 2^{x-1} \lt 1 \\ & \Rightarrow x-1 \lt 0 \\ & \Rightarrow-\infty \lt x \lt 1\end{aligned}\)
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