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The domain of definition of the function y (x) is given by the equation 2x+ 2y = 2 is : (A) 0< x≤1 (B) 0≤x≤1 (C) -∞ < x ≤0 (D) -∞< x<1
2^x +2^y =2, or, 2^y = 2 - 2^x
Take log with base 2 on both sides,
y=log(2-2^x),
For y to be real, 2 - 2^x > 0,
i.e., 2 > 2^x,
or, x < 1.
ANS is (D).
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