First slide

Algebra of real valued functions

Question

The domain of definition of function, y(x) given by the equation $2^{x} + 2^{y} = 2$ , is

Moderate

A

$0 < x \leq 1$
B

$0 \leq x \leq 1$
C

$0 < x < 1$
D

$- \infty < x < 1$

Solution

Given that,
$2^{x} + 2^{y} = 2, \forall x, y \in R$
$\Rightarrow$ $2^{y} = 2 - 2^{x}$
$\Rightarrow$ $y = \log_{2} (2 - x^{x}) f o r d o m a i n, 2 - 2^{x} > 0$
$\Rightarrow$ 2 > 2 x
$\Rightarrow$ x < 1
$\Rightarrow$ $x \in (- \infty, 1)$

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