Answer:
The tricky part is rewriting g(x + 2) as g(x) instead.
Start by substituting u = x + 2
u = x + 2
x = u - 2
Now we have:
g(u) = 3(u - 2) + 1
g(u) = 3u - 6 + 1
g(u) = 3u - 5
We have the function g with a single variable. So we could replace it back to x:
g(x) = 3x - 5
So the question becomes much simpler:
f(x) = 2x
g(x) = 3x - 5
To find f(g(x)), just put in g(x) = 3x - 5 into f(x)
f(x) = 2x
f(g(x)) = 2 * g(x)
f(g(x)) = 2(3x - 5)
f(g(x)) = 6x - 10
Answer:
6x - 10
g(x+2)=3x+1
