Find the Domain 3x^3-5x^2-10x+4 square root of 3x+1

Problem

ƒ(x)=(3*x3−5*x2−10*x+4)√(,3*x+1)

Solution

1. Identify the restrictions on the domain. The expression consists of a polynomial multiplied by a square root. Polynomials are defined for all real numbers, so the domain is restricted only by the square root.

2. Set up the inequality for the radicand. For a square root to result in a real number, the expression inside the radical must be greater than or equal to zero.

3*x+1≥0

3. Solve the inequality for x by subtracting 1 from both sides.

3*x≥−1

4. Divide both sides by 3 to isolate x

x≥−1/3

5. Express the domain in interval notation. The values of x start at −1/3 (inclusive) and go to infinity.

[−1/3,∞)

Final Answer

Domain: *[−1/3,∞)

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