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key term - Algebraic function

Definition

An algebraic function is a type of function defined as the root of a polynomial equation with coefficients in the real or complex numbers. It can be expressed using a finite number of operations involving addition, subtraction, multiplication, division, and taking roots.

5 Must Know Facts For Your Next Test

  1. Algebraic functions can include polynomial functions, rational functions, and root functions.
  2. The general form of an algebraic function is given by $P(y) = Q(x)$ where $P$ and $Q$ are polynomials.
  3. Not all algebraic functions are polynomials; for example, $\sqrt{x}$ is an algebraic function but not a polynomial.
  4. Algebraic functions are closed under addition, subtraction, multiplication, and composition but not necessarily under division unless the denominator is non-zero.
  5. Finding the inverse of an algebraic function may involve solving polynomial equations.

Review Questions

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