FunctionMedium
Question
The domain of definition of the function y (x) is given by the equation 2x + 2y = 2, is
Options
A.0 < x ≤ 1
B.0 ≤ x ≤ 1
C.- ∞ < x ≤ 0
D.- ∞ < x < 1
Solution
Given that, 2x + 2y = 2, ∀ x, y∈ R
But 2x, 2y > 0 ∀ x, y∈ R
Therefore, 2x = 2 - 2y < 2 ⇒ 0 < 2x < 2
Taking log on both sides with base 2 we get
log2 0 < log2 2x < log22
⇒ - ∞ < x < 1.
But 2x, 2y > 0 ∀ x, y∈ R
Therefore, 2x = 2 - 2y < 2 ⇒ 0 < 2x < 2
Taking log on both sides with base 2 we get
log2 0 < log2 2x < log22
⇒ - ∞ < x < 1.
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