Final answer:
To find (f/g)(x), we divide f(x) by g(x) by substituting their expressions into the given equation and simplifying the expression.
Step-by-step explanation:
To find (f/g)(x), we need to divide f(x) by g(x). Given that f(x) = 3√(4x) and g(x) = 2x + 3, let's substitute these into the expression.
(f/g)(x) = f(x)/g(x) = (3√(4x))/(2x + 3)
To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of (2x + 3), which is (2x + 3).
(f/g)(x) = (3√(4x))/(2x + 3) * (2x + 3)/(2x + 3) = (6x√(4x) + 9√(4x))/(4x + 6x + 6)
(f/g)(x) = (6x√(4x) + 9√(4x))/(10x + 6)
Therefore, (f/g)(x) = (6x√(4x) + 9√(4x))/(10x + 6).
Learn more about Division of Functions