A rational function is defined by f ( x ) = a ( x )

Pattab

Pattab

Answered question

2022-07-04

A rational function is defined by
f ( x ) = a ( x ) b ( x ) = a n x n + a n 1 x n 1 + + a 0 b m x m + a m 1 x m 1 + + b 0
where m , n N { 0 } such that not every coefficient b i is 0 and f(x) is not defined at the values of x for which b(x)=0.
What 'special' choice(s) of b(x) will give the result that the set of all polynomial functions, a ( x ) = a n x n + a n 1 x n 1 + + a 0 form a subset of the rational functions (as defined above)?

Answer & Explanation

Allison Pena

Allison Pena

Beginner2022-07-05Added 14 answers

Choose b m = b m 1 = = b 1 = 0 but b 0 = 1 so that b(x)=1.

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