The function R(x) - S(x) is [tex]3x^{3} -2x^{2} +x-1[/tex].
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) is called function.
According to the given question.
We have two functions
[tex]R(x) = 3x^{3} +2x^{2} +x[/tex]
And, [tex]S(x) = 4x^{2} + 1[/tex]
Therefore, the function R(x) - S(x) is given by
[tex]R(x) - S(x) = 3x^{3} +2x^{2} +x-(4x^{2} +1)[/tex]
[tex]\implies R(x) - S(x) = 3x^{3} +2x^{2} +x - 4x^{2} -1[/tex]
[tex]\implies R(x) - S(x) = 3x^{3} -2x^{2} +x-1[/tex]
Hence, function R(x) - S(x) is [tex]3x^{3} -2x^{2} +x-1[/tex].
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