when is g(g(x)) if g(x)=3x+4 then simplify answer and give the domain in interval notation
give interval notation step by step reasoning
To find g(g(x)), we first need to substitute g(x)=3x+4 into g(x).
g(g(x)) = g(3x+4) = 3(3x+4) + 4 = 9x + 12 + 4 = 9x + 16
Therefore, g(g(x)) = 9x + 16.
The domain of g(x) is all real numbers since the function is a linear function.
Therefore, the domain of g(g(x)) = 9x + 16 in interval notation is (-∞, ∞).