Functions 1 Question 7
7. The domain of definition of the function $y(x)$ is given by the equation $2^{x}+2^{y}=2$, is
(a) $0<x \leq 1$
(b) $0 \leq x \leq 1$
(c) $-\infty<x \leq 0$
(d) $-\infty<x<1$
(2000, 1M)
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Answer:
Correct Answer: 7. (c)
Solution:
- Given, $2^{x}+2^{y}=2, \forall x, y \in R$
But $\quad 2^{x}, 2^{y}>0, \forall x, y \in R$
Therefore, $2^{x}=2-2^{y}<2 \Rightarrow 0<2^{x}<2$
Taking log on both sides with base 2 , we get
$$ \log _2 0<\log _2 2^{x}<\log _2 2 \Rightarrow-\infty<x<1 $$
