Pregunta
Consider the function \( y=\sqrt{3 x-12} \) What are the domain and range of this function?
Ask by Maxwell Ingram. in the United States
Jan 26,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The domain of \( y=\sqrt{3x-12} \) is all real numbers \( x \) where \( x \geq 4 \), and the range is all non-negative real numbers \( y \) where \( y \geq 0 \).
Solución
Analyze the function features with analysis_type = range, expression = \( y=\sqrt{3 x-12} \).
Function by following steps:
- step0: Find the range:
\(y=\sqrt{3x-12}\)
- step1: Evaluate:
\(y\geq 0\)
The domain of the function \( y=\sqrt{3x-12} \) is all real numbers \( x \) such that \( x \geq 4 \), and the range of the function is all non-negative real numbers \( y \) such that \( y \geq 0 \).
Revisado y aprobado por el equipo de tutoría de UpStudy
Como
error msg
Explicar 
Simplifique esta solución Extra Insights
To determine the domain of the function \( y=\sqrt{3x-12} \), we need to ensure the expression under the square root is non-negative. This means: \[ 3x - 12 \geq 0 \] \[ 3x \geq 12 \] \[ x \geq 4 \] So, the domain is \( [4,\infty) \). Now, for the range, since \( y \) represents a square root function, it will always produce non-negative outputs. The minimum value happens when \( x = 4 \): \[ y = \sqrt{3(4) - 12} = \sqrt{0} = 0 \] As \( x \) increases, \( y \) can approach infinity. Thus, the range is \( [0,\infty) \). In summary, the domain is \( [4, \infty) \) and the range is \( [0, \infty) \).
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
