Question
Question: The domain of definition of the function f(x) given by the equation 2<sup>x</sup> + 2<sup>y</sup> = ...
The domain of definition of the function f(x) given by the equation 2x + 2y = 2 is
A
0 < x ≤ 1
B
0 ≤ x ≤ 1
C
−∞ < x ≤ 0
D
−∞ < x < 1
Answer
−∞ < x < 1
Explanation
Solution
It is given that 2x + 2y = 2 \overset{̶}{V}x, y ∈ R
But 2x. 2y > 0 \overset{̶}{V}x , y ∈ R
Therefore, 2x = 2 – 2y < 2
⇒ 0 < 2x < 2
Taking log for both side with base 2 ⇒ log2 0 < log22x < log22. Hence domain is −∞ < x < 1.