G(x)=\sqrt{x+3}g(x)= x+3 g, left parenthesis, x, right parenthesis, equals, square root of, x, plus, 3, end square root What i
1 answer:
Answer:
The domain of g(x) is -3 to infinity
Step-by-step explanation:
Given
Required
Determine the domain of g(x)
We start by expressing the content of the square root in the following form:
Subtract 3 from both sides
This can be expressed using interval notation as follows:
<em>Hence, the domain of g(x) is -3 to infinity</em>
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. With this consideration, we can continue.
(i) Let E the expression that we are analyzing:
Since (x-1)² is a perfect square, it is a positive number. So, E is a result of a sum of two positive numbers, 2(x-1)² and 3. Hence, E is a positive number, too.
(ii) Manipulating the expression:
So, it's the case when E=0. However, E is always a positive number. Then, there is no real number x that satisfies the expression.
8) Let E the expression that we want to calculate:
Multiplying by (2-1) in the both sides:
Repeating the process, we obtain:
(i) Let E the expression that we are analyzing:
Since (x-1)² is a perfect square, it is a positive number. So, E is a result of a sum of two positive numbers, 2(x-1)² and 3. Hence, E is a positive number, too.
(ii) Manipulating the expression:
So, it's the case when E=0. However, E is always a positive number. Then, there is no real number x that satisfies the expression.
8) Let E the expression that we want to calculate:
Multiplying by (2-1) in the both sides: