Are all polynomials rational functions? Are all algebraic functions polynomials?

Question
Rational functions
asked 2020-11-06
Are all polynomials rational functions? Are all algebraic functions polynomials?

Answers (1)

2020-11-07
It is known that all polynomials are not rational functions.
Example:
Consider the function \(f(x)=pi\). This, function is a polynomial but it cannot be written in the form of a rational function.
Hence, all polynomials are not rational functions.
Step 2
No, not all algebraic functions are polynomials.
If an algebraic expression has a radical, then it cannot be a polynomial.
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