Math - Domain of Composite function

Find the domain of the composite function f ₒ g . Please show all of your work.
f(x) = √x; g(x) = 2x + 12

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  1. f(x) = sqrt(x)
    g(x) = 2x + 12
    thus,
    (fog)(x) = sqrt(2x + 12)
    note that to get the domain, you must get the intersection of the 3 function domains.
    for f(x) = sqrt(x), x cannot be less than zero thus the domain is [0 , +infinity)
    for g(x) = 2x + 12, x can be any real number thus domain is (-infinity, +infinity).
    for (fog)(x) = sqrt(2x + 12), the lowest possible value of the radicand (term inside the radical sign) is zero. thus equating 2x + 12 to zero,
    2x + 12 = 0
    x = -6
    thus domain is [-6 , +infinity)

    the intersection of the three domains is therefore,
    [0, +infinity)

    hope this helps~ :)

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