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Function Composition definitions

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  • Function Composition
    Process of creating a new function by substituting one function into another, resulting in a combined operation.
  • Inside Function
    The function that is substituted into another function during composition, typically represented as g in f(g(x)).
  • Outside Function
    The function that receives another function as its input during composition, typically represented as f in f(g(x)).
  • Composite Function
    A function formed by applying one function to the results of another, often written as f(g(x)).
  • Notation
    A symbolic way to represent function composition, such as f(g(x)) or (f ∘ g)(x).
  • Domain
    The set of all input values for which a function or composite function is defined, considering restrictions from both functions.
  • Restriction
    A limitation on the input values of a function, often due to operations like division by zero or square roots of negatives.
  • Evaluation
    The process of finding the output of a function or composite function for a specific input value.
  • Decomposition
    The process of expressing a composite function as two or more simpler functions whose composition yields the original.
  • FOIL Method
    A technique for expanding the product of two binomials, often used when simplifying composed functions.
  • Shortcut Method
    An approach to evaluating composite functions by first evaluating the inside function at a value, then plugging the result into the outside function.
  • Simplification
    The process of reducing a function or expression to its most basic or compact form, often after composition.
  • Square Root Restriction
    A domain limitation that arises because the expression under a square root must be non-negative.
  • Fraction Restriction
    A domain limitation that occurs when the denominator of a fraction cannot be zero.
  • Polynomial
    An algebraic expression consisting of variables and coefficients, often resulting from composing or simplifying functions.