Pregunta
Find the domain of \( f(\mathrm{x}) \). \[ f(x)=\sqrt{9 x+36} \] Answer Attempt 1 out of 2 Answer Type: Interval
Ask by Montgomery Chandler. in the United States
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The domain of \( f(x) = \sqrt{9x + 36} \) is all real numbers \( x \) such that \( x \geq -4 \), which can be written as \([-4, \infty)\).
Solución
To find the domain of the function \( f(x) = \sqrt{9x + 36} \), we need to ensure that the expression inside the square root is non-negative.
**Step-by-Step Solution:**
1. **Set the expression inside the square root greater than or equal to zero:**
\[
9x + 36 \geq 0
\]
2. **Solve for \( x \):**
\[
9x \geq -36
\]
\[
x \geq -4
\]
3. **Write the domain in interval notation:**
\[
[-4, \infty)
\]
**Final Answer:**
\[
[-4,\ \infty)
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
Como
error msg
Explicar 
Simplifique esta solución Extra Insights
To find the domain of \( f(x) = \sqrt{9x + 36} \), we need to ensure that the expression inside the square root is non-negative. So, we set up the inequality: \[ 9x + 36 \geq 0 \] Solving this gives: \[ 9x \geq -36 \] \[ x \geq -4 \] Thus, the domain of the function is all values of \( x \) that are greater than or equal to -4. In interval notation, this is: \[ [-4, \infty) \] Now you've got the domain! Let's keep this math train rolling!🎉
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
