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Let f(x)=√3x and g(x)=x-6 What's the smallest number that is in the domain of fog?

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Answer:

6

Explanation:

Maybe you have ...

f(x) = √(3x)

g(x) = x-6

Then ...

f(g(x)) = √(3(x -6))

The square root function is only defined for non-negative arguments, so we require ...

3(x -6) ≥ 0

x -6 ≥ 0 . . . . . divide by 3

x ≥ 6 . . . . . . . . add 6

The smallest number in the domain of f(g(x)) is x = 6.

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