Pregunta
Find the domain of the function. \( f(x)=\sqrt{x-8} \) The domain of \( f(x) \) is \( \square \)
Ask by Evans Barrett. in the United States
Feb 25,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The domain of \( f(x) = \sqrt{x - 8} \) is all real numbers \( x \) where \( x \geq 8 \), which is written as [8, ∞).
Solución
To find the domain of the function f(x) = √(x - 8), we note that the expression under the square root must be non-negative because the square root of a negative number is not a real number. Therefore, set up the inequality:
x - 8 ≥ 0
Solving this, we get:
x ≥ 8
Thus, the domain of f(x) is all real numbers x such that x is greater than or equal to 8, which is expressed in interval notation as [8, ∞).
The domain of f(x) is [8, ∞).
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución Bonus Knowledge
To find the domain of \( f(x)=\sqrt{x-8} \), we need to ensure that the expression under the square root is non-negative. This means we want \( x - 8 \geq 0 \). Solving this gives \( x \geq 8 \). Therefore, the domain of \( f(x) \) is all real numbers greater than or equal to 8, expressed in interval notation as \( [8, \infty) \). Remember, when working with square roots, always check that the quantity inside is zero or positive to avoid complex numbers! Misinterpreting or overlooking this can lead to the domain being incorrectly defined, which means no real solutions for your function!
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
