Question
Find the domain of the rational function in interval notation. \( f(x)=\frac{x^{3}+x^{2}+3 x-2}{x-3} \)
Ask by Barrett Martin. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The domain of the function is all real numbers except 3, written as \( (-\infty, 3) \cup (3, \infty) \).
Solution
The function is given by f(x) = (x³ + x² + 3x - 2) / (x - 3). The domain consists of all real numbers except where the denominator is zero.
To find that value, set the denominator equal to zero:
x - 3 = 0 ⟹ x = 3.
Therefore, x cannot be 3. In interval notation, the domain is:
(-∞, 3) ∪ (3, ∞).
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Simplify this solution Mind Expander
To find the domain of the rational function \( f(x) = \frac{x^{3} + x^{2} + 3x - 2}{x - 3} \), we first need to identify any values that would make the denominator equal to zero since these values are not included in the domain. The denominator \( x - 3 = 0 \) when \( x = 3 \). Thus, the function is undefined at this point. The rest of the real numbers are included in the domain. Therefore, in interval notation, the domain of the function is: \[ (-\infty, 3) \cup (3, \infty) \]
