If the functions are defined as f(x) = √x and g(x) = √(1-x), then what is the common domain of the following functions: f + g, f - g, f/g, g/f, g - f where (f+g)(x) = f(x) + g(x), (f/g)(x) = f(x)/g(x)
If the functions are defined as f(x) = √x and g(x) = √(1-x), then what is the common domain of the following functions: f + g, f - g, f/g, g/f, g - f where (f+g)(x) = f(x) + g(x), (f/g)(x) = f(x)/g(x)
Option 1 -
0 ≤ x < 1
Option 2 -
0 < x < 1
Option 3 -
0 < x 1
Option 4 -
0 ≤ x ≤ 1
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1 Answer
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Correct Option - 4
Detailed Solution:f (x) + g (x) = √x + √1-x. The domain requires x ≥ 0 and 1-x ≥ 0, so x ≤ 1. Domain is [0,1].
f (x) - g (x) = √x - √1-x. Domain is [0,1].
f (x)/g (x) = √x / √1-x. Requires x ≥ 0 and 1-x > 0, so x < 1. Domain is [0,1).
g (x)/f (x) = √1-x / √x. Requires 1-x ≥ 0 and x > 0. Domain is (0,1].
The common domain for all these functional forms to be considered is (0,1).
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