Question

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

(a) 0 < x < 1 

(b) 0 < x ≤ 1 

(c) 0 ≤ x ≤ 1 

(d) None of these

Answer 1

Answer: (a) 0 < x < 1 

2^x + 2^y = 2 

⇒ 2^y = 2 – 2^x 

⇒ y log 2 = log (2 – 2^x ) 

⇒ The function will be defined only when 2 – 2^x > 0 

⇒ 2^x < 2¹ ⇒ x < 1 

Also, x > 0, y < 0 

∴ x ∈ (0, 1).