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Math  /  Algebra

QuestionConsider the following relation. −5y+x=2x+(x−3)2-5 y+\sqrt{x}=2 x+(x-3)^{2}
Step 3 of 3 : Determine the implied domain of the function found in the first step. Express your answer in interval inotation.
Answer

Studdy Solution

STEP 1

1. The relation given is −5y+x=2x+(x−3)2-5y + \sqrt{x} = 2x + (x-3)^2.
2. We need to determine the implied domain of this relation.
3. The domain is determined by the values of xx for which the expression is defined.
4. The square root function x\sqrt{x} is only defined for x≥0x \geq 0.

STEP 2

1. Identify the components of the equation that affect the domain.
2. Determine the conditions for each component to be defined.
3. Express the domain in interval notation.

STEP 3

Identify the components of the equation that affect the domain. The equation is:
−5y+x=2x+(x−3)2 -5y + \sqrt{x} = 2x + (x-3)^2
The component that affects the domain is x\sqrt{x}.

STEP 4

Determine the conditions for each component to be defined. For x\sqrt{x}, it is defined when:
x≥0 x \geq 0
This is because the square root function requires non-negative inputs to be defined in the real number system.

STEP 5

Express the domain in interval notation. Since xx must be greater than or equal to 0, the domain in interval notation is:
[0,∞) [0, \infty)
The implied domain of the function is [0,∞)\boxed{[0, \infty)}.

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