Q71 / 150 · MHT CET 2023 (11 May Shift 1) · Mathematics

The domain of the function given by $2^x+2^y=2$ is

  • A
    $0 < x \leq 1$
  • B
    $0 \leq x \leq 1$
  • C
    $-\infty < x \leq 0$
  • Correct answer
    D
    $-\infty < x < 1$

Solution

$\begin{aligned} & 2^x+2^y=2 \\ & \Rightarrow 2^y=2-2^x \\ & \Rightarrow y=\log _2\left(2-2^x\right) \text { is defined, if } 2-2^x>0 \\ & \Rightarrow 2^x < 2 \\ & \Rightarrow 2^{x-1} < 1 \\ & \Rightarrow x-1 < 0 \\ & \Rightarrow-\infty < x < 1\end{aligned}$

Hence, the correct answer is option: 'D'.

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