Respuesta :
The domain is the set of all real numbers, i.e.,
-∞ < x < ∞ or x ∈ (-∞, ∞) or x ∈ R.
The range is the set of all real numbers, i.e.,
-∞ < y < ∞ or y ∈ (-∞, ∞) or y ∈ R.
Further explanation
The domain of a function is the set of all values that can be plugged into a function and have the function defined. Besides that, the function has a real number for a value.
Given the function f(x) = 3x + 5. This function is a line function, that is, the simplest polynomial function. The polynomial functions have any real number as their domain.
In our problem, there are no restrictions on the domain (x value). Therefore, this line is continuous for all real values of x.
Hence, in all notations, the domain is the set of all real numbers, i.e.,
- [tex]\boxed{ \ -\infty < x < \infty \ }[/tex], or
- [tex]\boxed{ \ x \ \epsilon \ (-\infty, \infty) \ }[/tex], or
- [tex]\boxed{ \ x \ \epsilon \ R \ }[/tex]
The range of a function is the set of all possible values that a function can take.
This is a line with a slope is 3, so this is not a horizontal line that has a fixed value.
Hence, in all notations, the range is the set of all real numbers, i.e.,
- [tex]\boxed{ \ -\infty < y < \infty \ }[/tex], or
- [tex]\boxed{ \ y \ \epsilon \ (-\infty, \infty) \ }[/tex], or
- [tex]\boxed{ \ y \ \epsilon \ R \ }[/tex]
Learn more
- The range of the given function https://brainly.com/question/1435353
- Determine the domain of the composite function brainly.com/question/3852778
- If f(x) = x² – 2x and g(x) = 6x + 4, for which value of x does (f o g)(x) = 0? brainly.com/question/1774827
Keywords: what are, the domain and range, the function f(x) = 3x + 5, all real numbers, line, slope, defined
