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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.