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The domain of definition of the function...

The domain of definition of the function `f(x)` given by the equation `2^y=2-2^x` is `0

A

`0 lt x le 1`

B

`0 le x le 1`

C

`-infty lt x le 0`

D

`-infty lt x lt 1`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `2^(x)+2^(y)=2, AA x , y in R`
But `2^(x),2^(y) gt 0, AA x,y in R`
Therefore, `2^(x)=2-2^(y) lt 2 rArr 0 lt 2^(x) lt 2`
Talking log on both sides with base 2, we get
`log_(2)0 lt log_(2) 2^(x) lt log_(2)2 rArr -oo lt x lt 1`
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