To find f(g(x)), we need to substitute g(x) into the function f(x). Let’s start by writing down what each function looks like.
We have:
- f(x) = log2(3x + 9)
- g(x) = log2(x + 3)
Now, we can substitute g(x) into f(x):
f(g(x)) = f(log2(x + 3))This implies we need to replace the x in f(x) with g(x):
f(g(x)) = log2(3 * log2(x + 3) + 9)This expression simplifies to:
f(g(x)) = log2(3log2(x + 3) + 9)In conclusion, the composition of the two functions, f(g(x)), is given by:
f(g(x)) = log2(3 * log2(x + 3) + 9)