Agar fungsi \( \displaystyle f(x) = \sqrt{ \frac{3x^2+2x-8 }{x+2} } \) terdefinisi maka daerah asal \( f(x) \) adalah…
- \( \{ x \ | \ x \leq -\frac{4}{3}, \ x \neq -2, \ x \in R \} \)
- \( \{ x \ | \ x \geq \frac{4}{3}, \ x \in R \} \)
- \( \{ x \ | \ x \geq -2, \ x \in R \} \)
- \( \{ x \ | \ -2 < x \leq \frac{4}{3}, \ x \in R \} \)
- \( \{ x \ | \ x < -2, \ \text{atau} \ x \geq \frac{4}{3}, \ x \in R \} \)
(UN 2019 IPA)
Pembahasan:
Syarat agar fungsi di atas terdefinisi, yaitu:
\begin{aligned} \frac{3x^2+2x-8 }{x+2} \geq 0 \\[8pt] \frac{(3x-4)(x+2)}{x+2} \geq 0 \\[8pt] 3x-4 \geq 0 \\[8pt] x \geq \frac{4}{3} \end{aligned}
Jadi, fungsi \(f(x)\) terdefinisi jika daerah asalnya \( \{ x \ | \ x \geq \frac{4}{3}, \ x \in R \} \).
Jawaban B.