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

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

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