Respuesta :
3x + 4 cannot be negative because of the square root so
3x + 4 >= 0 and x >= -4/3 This is the domain (answer)
The range-
when x = -4/3 y = -5 The range is y>= -5 answer
In interval notation domain = [-4/3, ∞) and range = [-5, ∞)
3x + 4 >= 0 and x >= -4/3 This is the domain (answer)
The range-
when x = -4/3 y = -5 The range is y>= -5 answer
In interval notation domain = [-4/3, ∞) and range = [-5, ∞)
Using it's concepts, it is found that:
- The domain is given by: [tex]x \geq \frac{4}{3}[/tex].
- The range is [tex]y \geq -5[/tex].
What are the domain and the range of a function?
- The domain of a function is the set that contains all the values of the input.
- The range of a function is the set that contains all the values of the output.
In this problem, the function is:
[tex]y = 2\sqrt{3x + 4} - 5[/tex]
It is an even root, hence the term inside the root cannot be negative, meaning that the domain is given by:
[tex]3x + 4 \geq 0 \rightarrow x \geq \frac{4}{3}[/tex]
The range of the square root function is [tex]y \geq 0[/tex], however, considering the translation, it is [tex]y \geq -5[/tex].
More can be learned about the domain and the range of a function at https://brainly.com/question/10891721
