Respuesta :
Answer:
all real numbers except -1 and 1
Next question is the first two boxes “infinity & negative infinity” on edge.
Step-by-step explanation:
The domain of the given function is [tex]\rm (-\infty,-1)\cup(-1,1)\cup(1,\infty)[/tex] and the range of the given function is [tex]\rm (-\infty,\infty)[/tex] and this can be determined by using the given data.
Given :
[tex]\rm f(x) = \dfrac{2x}{3x^2-3}[/tex]
The following steps can be used in order to determine the domain and range of the given function:
Step 1 - Write the given function.
[tex]\rm f(x) = \dfrac{2x}{3x^2-3}[/tex]
Step 2 - Domain is the values of x in the function f(x) and the range is the values of f(x).
Step 3 - Simplify the given function.
[tex]\rm f(x) = \dfrac{2x}{3(x^2-1)}[/tex]
[tex]\rm f(x) = \dfrac{2x}{3(x-1)(x+1)}[/tex]
Step 4 - So, the domain of the given function is [tex]\rm (-\infty,-1)\cup(-1,1)\cup(1,\infty)[/tex].
Step 5 - The range of the given function is [tex]\rm (-\infty,\infty)[/tex].
For more information, refer to the link given below:
https://brainly.com/question/2253924
