For the functions \(f(x)=4x+12\) and \(g(x)=\dfrac{1}{x}\), what is the set of real numbers \(x\) on which \(g(f(x))\) is defined?

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$$ g(f(x)) = \frac{1}{4x+12} $$

This composite function is undefined when the denominator is \(0\).

$$ 4x+12 \neq 0 $$ $$ 4x \neq -12 $$ $$ x \neq \boxed{-3} $$