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Math Help - Composite Functions

  1. #1
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    Composite Functions

    Use the concept of composite functions to explain why h(x) = |x^2 - 4x - 6| is a continuous function.

    g(x) = |x|
    f(x) = x^2 - 4x - 6

    These are both continuous, f because of the properties of continuous functions, the absolute value of g is continues too, so the composite is continuous. If f is continuous at c and g is continuous at f(c), then the composite g o f is continuous at c.

    Did i do this right?
    Thanks.
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  2. #2
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    Quote Originally Posted by Sxon View Post
    Use the concept of composite functions to explain why h(x) = |x^2 - 4x - 6| is a continuous function.

    g(x) = |x|
    f(x) = x^2 - 4x - 6

    These are both continuous, f because of the properties of continuous functions, the absolute value of g is continues too, so the composite is continuous. If f is continuous at c and g is continuous at f(c), then the composite g o f is continuous at c.

    Did i do this right?
    Thanks.

    Sounds fine to me. Only stress that c is ANY real point, and thus h(x) is continuous everywhere.

    Tonio
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