Find the Domain

Problem

(3√(,27*x^27))/(3*x^(−2))⋅((−3*x)^3)/(3*x^(−1))

Solution

1. Identify the constraints for the square root function. For the expression √(,27*x^27) to be defined in the set of real numbers, the radicand must be non-negative.

27*x^27≥0

2. Solve the inequality for x Since 27 is positive and the exponent 27 is odd, the term x^27 is non-negative if and only if x is non-negative.

x≥0

3. Identify the constraints for the denominators. The expressions in the denominators, 3*x^(−2) and 3*x^(−1) must not equal zero.

3*x^(−2)≠0

3*x^(−1)≠0

4. Analyze the division by zero constraints. Both x^(−2)=1/(x^2) and x^(−1)=1/x are undefined at x=0 Furthermore, if x≠0 these terms can never equal zero. Thus, we must exclude x=0

x≠0

5. Combine the requirements. The square root requires x≥0 and the denominators require x≠0 The intersection of these conditions is x>0

x>0

Final Answer

Domain: *{[x∈ℝ,x>0]}

Want more problems? Check here!