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Composition of Functions quiz

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이 집합의 용어 (15)

  • What does function composition involve?
    Function composition involves substituting one function into another, such as f(g(x)), to create a new expression or function.
  • How do you evaluate f(7) for f(x) = x^2 + 3x - 10?
    Replace all x's with 7, calculate 7^2 + 3*7 - 10, which equals 60.
  • What is the result of composing f(x) = x^2 + 3x - 10 with g(x) = x - 2 to find f(g(x))?
    Replace x in f(x) with g(x), giving (x - 2)^2 + 3(x - 2) - 10, which simplifies to x^2 - x - 12.
  • How is the notation f ∘ g(x) interpreted?
    It means f(g(x)), where g(x) is the inside function and f(x) is the outside function.
  • What is f(g(x)) for f(x) = x + 4 and g(x) = x^2 - 3?
    Replace x in f(x) with g(x), resulting in x^2 - 3 + 4, which simplifies to x^2 + 1.
  • How do you find g(f(x)) for f(x) = x + 4 and g(x) = x^2 - 3?
    Replace x in g(x) with f(x), giving (x + 4)^2 - 3, which simplifies to x^2 + 8x + 13.
  • What is the first step in evaluating a composed function at a number?
    Compose the functions to get a new function, then substitute the number into the composed function.
  • How do you use the shortcut method to evaluate f(g(3)) for f(x) = x^2 and g(x) = x - 1?
    First, evaluate g(3) = 2, then substitute 2 into f(x), so f(2) = 4.
  • Why can't the shortcut method always be used for evaluating composed functions?
    Because sometimes you are required to find the composed function f(g(x)) before substituting a value.
  • What is the domain restriction for g(x) = sqrt(x)?
    x must be greater than or equal to 0, since the radicand cannot be negative.
  • What additional domain restriction arises when composing f(x) = 1/(x - 2) with g(x) = sqrt(x)?
    The denominator sqrt(x) - 2 cannot be zero, so sqrt(x) ≠ 2, which means x ≠ 4.
  • How do you combine domain restrictions for composed functions?
    Find restrictions for the inside function, then for the composed function, and combine them to get the total domain.
  • What is the domain of f(g(x)) for f(x) = 1/(x - 2) and g(x) = sqrt(x)?
    The domain is x ≥ 0, x ≠ 4; in interval notation, [0, 4) ∪ (4, ∞).
  • What is the FOIL method used for in function composition?
    The FOIL method is used to expand binomials when simplifying composed functions, such as (x + 4)^2.
  • When composing functions, which function is considered the 'inside' function?
    The function written second in the composition, such as g in f(g(x)), is the inside function.