Find the Domain x^3.5

Problem

x3.5

Solution

1. Rewrite the exponent as a fraction to better understand the constraints of the function.

x3.5=x(7/2)

2. Identify the radical form of the expression, which involves a square root because the denominator of the exponent is 2

x(7/2)=√(,x7)

3. Determine the restriction for an even root. The expression inside a square root must be greater than or equal to zero for the result to be a real number.

x7≥0

4. Solve the inequality. Since raising a number to an odd power preserves its sign, the condition simplifies to x being non-negative.

x≥0

Final Answer

Domain of *x3.5={[x∈ℝ,x≥0]}

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