Q67 / 150 · MHT CET 2024 (10 May Shift 1) · Mathematics

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
    $-\infty \lt x \leq 0$
  • Correct answer
    D
    $-\infty \lt x \lt 1$

Solution

$\begin{aligned} & 2^x+2^y=2 \\ & \Rightarrow 2^y=2-2^x \\ & \Rightarrow y=\log _2\left(2-2^x\right) \text { is defined, if } 2-2^x\gt0 \\ & \Rightarrow 2^x \lt 2 \\ & \Rightarrow 2^{x-1} \lt 1 \\ & \Rightarrow x-1 \lt 0 \\ & \Rightarrow-\infty \lt x \lt 1\end{aligned}$

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

Relevant Questions