To find f(g(x)), we need to substitute g(x) into the function f(x).
We have:
- f(x) = 2x + 1
- g(x) = x + 2
Now, we substitute g(x) into f:
f(g(x)) = f(x + 2)
Now, replace x in f(x) with (x + 2):
f(x + 2) = 2(x + 2) + 1
Next, we simplify this expression:
f(x + 2) = 2x + 4 + 1
So, f(x + 2) = 2x + 5.
Therefore, f(g(x)) = 2x + 5.