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Composition of Functions definitions

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  • Function Composition
    Process of substituting one function into another, resulting in a new expression with combined operations.
  • Composite Function
    Resulting expression after one function is substituted into another, often simplified to a polynomial.
  • Inside Function
    Expression placed within another function during composition, determining the initial substitution.
  • Outside Function
    Expression receiving the substitution during composition, dictating the final structure.
  • Notation
    Symbolic representation of composition, often written as f(g(x)) or with a small circle between function names.
  • Polynomial
    Algebraic expression formed by combining composed functions, typically simplified using algebraic methods.
  • FOIL Method
    Technique for expanding binomials, used to simplify expressions resulting from function composition.
  • Evaluation
    Process of substituting a specific value into a function or composite function to obtain a numerical result.
  • Shortcut Method
    Alternative approach for evaluating composed functions by sequentially substituting values, saving time in some cases.
  • Descending Powers
    Arrangement of terms in a polynomial from highest to lowest exponent, often seen after simplifying compositions.
  • Coefficient
    Numerical factor multiplying a variable in a polynomial, affected by composition and simplification.
  • Degree
    Highest exponent in a polynomial, indicating the complexity of the composed function.
  • Substitution
    Replacement of variables or expressions within a function, central to the process of composition.
  • Sequential Evaluation
    Stepwise process of evaluating the inside function first, then using its result in the outside function.
  • Simplification
    Reduction of composed expressions to their most concise form, often involving combining like terms and expanding.