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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` is `0

A

`0 lt x le 1`

B

` 0 le x le 1`

C

`-oo lt x le 0`

D

`-oo lt x lt 1`

Text Solution

Verified by Experts

The correct Answer is:
D
It is given that `2^(x)+2^(y)=2 AA x,y in R`
or `2^(y)=2-2^(x)`
or `y=log_(2)(2-2^(x))`
Therefore, function id defined only when `2-2^(x) gt 0 " or " 2^(x) lt 2 " or " x lt 1`.
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