Given: 2x+2y = 2 We have to find the domain of function y (x). Now, 2x+2y = 2 ⇒ 2y = 2 - 2x ... (i) Taking logarithmic of both sides we have log(2y) = log (2−2x) ⇒ y log 2 = log (2−2x) [Using properties of logarithmic function 3] ⇒ y =
log(2−2x)
log‌2
= log2(2−2x) Using definition of logarithmic function , y (x) is defined for 2 - 2x > 0 ⇒ 2x < 2 = 21 ⇒ x < 1 ∴ domain of y (x) = (- ∞ , 1) Hence, option 'D' is correct.