Find the Domain y=1/3x

Problem

y=1/(3*x)

Solution

1. Identify the type of function. This is a rational function where the variable x is in the denominator.

2. Determine the restriction for the domain. For a rational function to be defined, the denominator cannot be equal to zero.

3. Set up the inequality to find the excluded value.

3*x≠0

4. Solve for x by dividing both sides by 3

x≠0

5. State the domain in interval notation. The domain includes all real numbers except 0

(−∞,0)∪(0,∞)

Final Answer

Domain:{[x∈ℝ,x≠0]}

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