Question

The domain of definition of the function y(x) is given by the equation 2^x + 2^y = 2 is 

(a) 0 < x ≤ 1 

(b) 0 ≤ x ≤ 1 

(c) –∞ < x ≤ 0 

(d) –∞ < x < 1

Answer 1

Correct option (d) –∞ < x < 1

Explanation:

Given equation is 2x + 2y = 2

⇒ 2y = 2 – 2x

⇒ y = log₂(2 – 2x )

It is defined for (2 – 2x ) > 0

⇒ 2x < 2 = 21

⇒ x < 1

Thus, D_f = (–∞, 1)