SATHEE: Functions 1 Question 7

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) $0 \leq x \leq 1$

(d) $- \infty < x < 1$

(2000, 1M)

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Answer:

Correct Answer: 7. (d)

Solution:

Given, $2^{x} + 2^{y} = 2, \forall x, y \in R$

But $2^{x}, 2^{y} > 0, \forall x, y \in R$

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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Functions 1 Question 7

7.

Answer:

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