If f(x)=√x-7 and g(x)=-3x-6, which statement is true? -3 is the domain of f°g -3 is not the domain of f°g

Question

If f(x)=√x-7 and g(x)=-3x-6, which statement is true?

-3 is the domain of f°g

-3 is not the domain of f°g

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    2021-09-21T00:06:15+00:00

    (f∘g)(x) = √((-3x -6) -7) = √(-3x -13)

    We require
    .. -3x -13 ≥ 0
    .. -13 ≥ 3x
    .. x ≤ -13/3
    .. x ≤ -4 1/3

    -3 is NOT in the domain of f∘g.

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