5 2 study guide and intervention composition of functions


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1-7 Study Guide and Intervention (continued) Functions Find Function Values Equations that are functions can be written in a form called function notation

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STEP 4 Write the potential energy function as a composition of the functions for height and potential energy p(h) = m · g · h p(h(t)) = 2000 · 9 8 

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Function Values Equations that are functions can be written in a form called function notation For example y 2x 1 can be written as f(x) 2x 1 In the 

  • Is FGX equal to GFX?

    In general gf(x) is not equal to fg(x).

  • In order to evaluate a composite function, take the given input value (fractional value) and find its output value (which may be a fraction).
    Then, take this output value and replace it as the "new" input value ("new" fractional value) of a second function, to find the value between the composition.

  • What is an example of a composition function?

    In the composition of (f o g) (x) the domain of function f becomes g(x).
    The domain is a set of all values which go into the function.
    Example: If f(x) = 3x+1 and g(x) = x2 , then f of g of x, f(g(x)) = f(x2) = 3x2+1.

  • What does this mean f ∘ G?

    In the composition of functions we substitute an entire function into another function.
    The notation of the function f with g is (f∘g)(x)=f(g(x)) and is read f of g of x .
    It means that wherever there is an x in the function f , it is replaced with the function g(x) .

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