Find the Domain (24x^3+2x^2+23x+2)/(6x-1)

Problem

(24*x^3+2*x^2+23*x+2)/(6*x−1)

Solution

1. Identify the type of function. This is a rational function, which is defined for all real numbers except where the denominator is equal to zero.

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

6*x−1=0

3. Solve for x by adding 1 to both sides and then dividing by 6

6*x=1

x=1/6

4. State the domain as all real numbers except the value that makes the denominator zero. In interval notation, this excludes 1/6

Final Answer

Domain:(−∞,1/6)∪(1/6,∞)

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