Find the Domain Q=50-5p

Problem

Q=50−5*p

Solution

1. Identify the type of function. The expression Q=50−5*p is a linear function where Q is the dependent variable and p is the independent variable.

2. Determine mathematical constraints. In a pure mathematical context, a linear polynomial has no restrictions (no denominators that could be zero and no even roots of negative numbers).

3. Consider economic context. Since Q usually represents quantity and p represents price, both variables must typically be non-negative (p≥0 and Q≥0.

4. Solve for the upper bound of p by setting Q≥0

50−5*p≥0

−5*p≥−50

p≤10

5. Combine the constraints to find the interval for p

Final Answer

Domain: *{[p∈ℝ,0≤p≤10]}

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