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26 August, 23:59

Let f (x) = x^2-16 and g (x) = x+4. Find f/g and it's domain

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  1. 27 August, 00:05
    0
    f/g = (x+4)

    Step-by-step explanation:

    f*g means multiply the functions.

    (x^2-16) (x-4) = x^3-4x^2-16x+64.

    f/g means divide the functions

    (x^2-16) / (x-4), but the numerator is a difference of squares, (x+4) (x-4), and the last cancels the denominator.

    f/g = (x+4)

    Domains of a composite function are the domains that satisfy both.

    f (x) has domain of all reals.

    g (x) does too.

    Their composite domain is all reals

    In the second, the denominator is (x-4).

    The function doesn't exist at x=4, regardless of what can be factored. Therefore,

    the domain of f/g is all reals except x=4.
  2. 27 August, 00:09
    0
    Step-by-step explanation:

    f (x) = x^2-16 and g (x) = x+4

    f/g = (x² - 16) / (x + 4)

    = (x + 4) (x - 4) / (x + 4)

    = x - 4
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