Find the Domain 2/(x^-9.5)

Problem

ƒ(x)=2/(x(−9.5))

Solution

1. Rewrite the expression using the definition of negative exponents, a(−n)=1/(an) to see the structure of the function.

ƒ(x)=2*x9.5

2. Convert the decimal exponent to a fraction to identify potential restrictions such as roots.

ƒ(x)=2*x19/2

3. Identify the radical form of the expression, which is 2√(,x19)

ƒ(x)=2√(,x19)

4. Determine the restriction for an even root (square root), which requires the radicand to be non-negative.

x19≥0

5. Solve the inequality for x Since the power is odd, the inequality holds true for all non-negative values of x

x≥0

Final Answer

Domain:[0,∞)

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