Find the domain of the following function.
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2^x + 2^y = 2
2^x is always positive. 2^(⁻∞) approaches 0.
2^1 is 2.
same with 2^y.
Hence 0 < 2^x < 2 => -∞ < x < 1
0 < 2^y < 2 => -∞ < y < 1
Domain : x ∈ (-∞, 1) , y ∈ (-∞, 1)
2^x is always positive. 2^(⁻∞) approaches 0.
2^1 is 2.
same with 2^y.
Hence 0 < 2^x < 2 => -∞ < x < 1
0 < 2^y < 2 => -∞ < y < 1
Domain : x ∈ (-∞, 1) , y ∈ (-∞, 1)
kvnmurty:
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2^x + 2^y =2
2^y= 2 -2^x
take log(base 2 ) both side
y =log{ ( 2 - 2^x) base 2}
we know log will be defined
when
( 2 -2^x ) > 0
2 > 2^x
we know exponential is always positive function.
so, not sign change when remove 2
2 > 2^x
1 > x
hence ,
Domain € ( -infinity , 1)
€ means belongs to
2^y= 2 -2^x
take log(base 2 ) both side
y =log{ ( 2 - 2^x) base 2}
we know log will be defined
when
( 2 -2^x ) > 0
2 > 2^x
we know exponential is always positive function.
so, not sign change when remove 2
2 > 2^x
1 > x
hence ,
Domain € ( -infinity , 1)
€ means belongs to
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