Find the Domain u-2 = square root of -2u+39

Problem

u−2=√(,−2*u+39)

Solution

1. Identify the restriction for the square root function. For the expression to be defined in the set of real numbers, the radicand (the expression inside the square root) must be greater than or equal to zero.

−2*u+39≥0

2. Solve the inequality for u by subtracting 39 from both sides.

−2*u≥−39

3. Divide both sides by −2 Remember that dividing by a negative number reverses the inequality sign.

u≤39/2

4. Identify the restriction for the left side of the equation. Since the principal square root is always non-negative, the expression u−2 must also be greater than or equal to zero.

u−2≥0

5. Solve for u by adding 2 to both sides.

u≥2

6. Combine the two inequalities to find the intersection of the conditions.

2≤u≤39/2

Final Answer

Domain:[2,19.5]

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