Find the Domain x^0.3=-0.76

Problem

x0.3=−0.76

Solution

1. Identify the nature of the exponent. The exponent 0.3 can be written as a fraction in simplest form.

0.3=3/10

2. Rewrite the equation using radical notation to analyze the domain of the power function.

x3/10=√(10,x3)

3. Determine the restriction for an even root. Since the denominator of the exponent is 10 (an even number), the expression √(10,x3) is only defined for non-negative values in the set of real numbers.

x3≥0

4. Solve the inequality for x Since the cube of a number is non-negative if and only if the number itself is non-negative, we find the domain.

x≥0

5. Evaluate the equation's consistency with the domain. The expression x0.3 will always produce a non-negative result for any x in its domain (x≥0. Since the right side of the equation is −0.76 there are no real values of x that satisfy the equation, but the domain of the function ƒ(x)=x0.3 remains restricted to non-negative reals.

Final Answer

Domain: *[0,∞)

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