The function R(x) + S(x) exists given by [tex]3x^3+6x^2+x+1[/tex].
An expression, rule, or law that describes a relationship between one variable (independent variable) and another variable (dependent variable) exists named a function.
Let the functions be [tex]R(x)=3x^3+2x^2+x[/tex] and [tex]S(x)=4x^2+1.[/tex]
Adding both of the equations, we get
[tex]$R(x)+S(x)=(3x^3+2x^2+x) +(4x^2+1)[/tex]
simplifying both of the equations we get
[tex]$R(x)+S(x)=3x^3+2x^2+x+4x^2+1[/tex]
[tex]=3x^3+6x^2+x+1[/tex]
Therefore, the function R(x) + S(x) exists given by [tex]3x^3+6x^2+x+1[/tex].
To learn more about function refer to:
brainly.com/question/12431044
#SPJ9
