Questions: Find the domain of the following function. f(x) = (x-2)/(x+1)

Transcript text: Find the domain of the following function. \[ f(x)=\frac{x-2}{x+1} \]

Solution

Step 1: Identify the Denominator Polynomial Q(x)

The denominator polynomial is \(Q(x) = x + 1\).

Step 2: Find the Roots of Q(x)

The roots of \(Q(x)\) are: \( \left\{-1\right\} \).

Step 3: Domain of the Function

The domain of \(f(x) = \frac{x - 2}{x + 1}\) is \( \left(-\infty, -1\right) \cup \left(-1, \infty\right) \).

Step 4: Check for Simplification

No simplification possible. The domain remains the same.

The domain of \(f(x)\) is \( \left(-\infty, -1\right) \cup \left(-1, \infty\right) \), rounded to 2 decimal places.

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