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Function Composition definitions Flashcards

Function Composition definitions
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  • Function Composition
    Process of creating a new function by substituting one function into another, often written as f(g(x)).
  • Composite Function
    Resulting function formed when the output of one function becomes the input of another.
  • Inside Function
    Function that is substituted into another function during composition, typically represented as g(x) in f(g(x)).
  • Outside Function
    Function that receives the output of another function as its input in a composition, such as f(x) in f(g(x)).
  • Domain
    Set of all input values for which a function or composite function is defined, considering all restrictions.
  • Restriction
    Condition that limits the allowable input values for a function, often due to operations like division or square roots.
  • Notation
    Standardized way of representing mathematical concepts, such as f(g(x)) or (f∘g)(x) for composition.
  • Evaluation
    Process of finding the output of a function or composite function for a specific input value.
  • Decomposition
    Reverse process of composition, expressing a single function as a combination of two or more simpler functions.
  • FOIL Method
    Technique for expanding products of binomials, often used when simplifying expressions in function composition.
  • Square Root
    Mathematical operation that finds a value which, when multiplied by itself, gives the original number; introduces domain restrictions.
  • Fraction
    Expression representing division, where the denominator cannot be zero, affecting the domain of functions.
  • Simplification
    Process of reducing a mathematical expression to its most concise and manageable form.
  • Polynomial
    Algebraic expression consisting of variables and coefficients, often resulting from composing or simplifying functions.
  • Shortcut Method
    Alternative approach for evaluating composite functions by first evaluating the inner function at a value, then using this result in the outer function.