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. (d)

Solution:

  1. 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 $



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