Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsDomain-RangeEasy2 minQB

MathematicsEasysingle choice

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

Answer:

Solution:

It is given that $2^{x} + 2^{y} = 2\forall x, y \in R$

Therefore, $2^{x} = 2 - 2^{y} < 2 \Rightarrow 0 < 2^{x} < 2$

Taking $lo g$ for both side with base 2 .

$\Rightarrow lo g_{2} 0 < lo g_{2} 2^{x} < lo g_{2} 2$

Hence domain is $- \infty < x < 1$ .

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Domain-Range

⏱ 2mℹ️ Source: QB

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