Find the Domain (36x^5-30x^3+9x^2)/(6x^2)

Problem

(36*x5−30*x3+9*x2)/(6*x2)

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 of x

6*x2=0

3. Solve for x by dividing both sides by 6 and taking the square root.

x2=0

x=0

4. Determine the domain by excluding the value found in the previous step from the set of all real numbers. The function is defined for all x≠0

5. Express the domain in interval notation.

(−∞,0)∪(0,∞)

Final Answer

Domain:(−∞,0)∪(0,∞)

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