First slide

Functions (XII)

Question

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

Moderate

A

$0 < x \leq 1$
B

$0 \leq x \leq 1$
C

$- \infty < x \leq 0$
D

$- \infty < x < 1$

Solution

It is given that $2^{x} + 2^{y} = 2 \forall x, y \in R$
$\begin{array}{l} or 2^{y} = 2 - 2^{x} \\ or y = \log_{2} (2 - 2^{x}) \end{array}$
Therefore, function is defined only when
$\begin{array}{l} 2 - 2^{x} > 0 or 2^{x} < 2 \\ or x < 1 . \end{array}$

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