Functions Question 376
Question: The domain of two definition of the function $ f(x) $ is given by the equation $ 2^{x}+2^{y}=2 $ is
Options:
A) $ 0<x\le 1 $
B) $ 0\le x\le 1 $
C) $ -\infty <x\le 0 $
D) $ -\infty <x<1 $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] We have, $ 2^{x}+2^{y}=2\Rightarrow 2^{y}=2-2^{x} $
$ \Rightarrow y={\log_2}(2-2^{x})\Rightarrow 2-2^{x}>0 $ (
$ \therefore $ y is real)
$ \Rightarrow 2^{x}<2\Rightarrow {2^{x-1}}<1\Rightarrow x-1<0\Rightarrow x<1 $
$ \Rightarrow -\infty <x<1 $
BETA
