Find the Domain f(x)=4x^2+1/x

Problem

ƒ(x)=4*x2+1/x

Solution

1. Identify the components of the function. The function ƒ(x) consists of a polynomial term 4*x2 and a rational term 1/x

2. Determine the restrictions for each part. Polynomials are defined for all real numbers. Rational expressions are undefined when the denominator is equal to zero.

3. Set the denominator of the rational term to zero to find the excluded value.

x=0

4. State the domain by excluding the value that makes the denominator zero. The domain consists of all real numbers except x=0

Final Answer

Domain: *(−∞,0)∪(0,∞)

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