Find the Domain 17.2x^12.86

Problem

17.2*x12.86

Solution

1. Identify the type of function. The expression 17.2*x12.86 is a power function of the form ƒ(x)=a*xn

2. Analyze the exponent. The exponent 12.86 is a positive terminating decimal. This can be expressed as a fraction in simplest form: 12.86=1286/100=643/50

3. Determine the constraints based on the exponent. For a power x(p/q) if q is even, the base x must be non-negative (x≥0 to avoid imaginary numbers. Since the denominator of the simplified exponent is 50 (an even number), the function is only defined for non-negative real numbers.

4. State the domain. The values of x must be greater than or equal to 0

Final Answer

Domain: *[0,∞)

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