Find the Domain f(x)=(x^3-x^2+1)/(|x|)

Problem

ƒ(x)=(x3−x2+1)/|x|

Solution

1. Identify the restriction for a rational function, which is that the denominator cannot be equal to zero.

2. Set the denominator equal to zero to find the excluded values of x

|x|=0

3. Solve for x by noting that the absolute value of a number is zero if and only if the number itself is zero.

x=0

4. Determine the domain by excluding the value x=0 from the set of all real numbers.

5. Express the domain in interval notation as the union of all values less than zero and all values greater than zero.

Final Answer

Domain: *(−∞,0)∪(0,∞)

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