Questions: Find the domain of the function. f(x) = 6 - 1/x^3

Transcript text: Find the domain of the function. \[ f(x)=6-\frac{1}{x^{3}} \]

Solution

Solution Steps

Step 1: Identify the Function

We are given the function \( f(x) = 6 - \frac{1}{x^3} \).

Step 2: Determine Where the Function is Undefined

To find the domain, we need to identify where the function is undefined. The function is undefined when the denominator of the fraction is zero, which occurs when \( x^3 = 0 \).

Step 3: Solve for Undefined Values

Solving the equation \( x^3 = 0 \) gives us \( x = 0 \). Therefore, the function is undefined at this point.

Step 4: State the Domain

The domain of the function is all real numbers except the point where the function is undefined. Thus, the domain can be expressed as \( \mathbb{R} \setminus \{0\} \), or in words, all real numbers except \( x = 0 \).

Final Answer

\(\boxed{\mathbb{R} \setminus \{0\}}\)

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