Question #402e2

1 Answer
Jan 25, 2018

f@g(2)=9

Explanation:

f@g is read "f of g of x". It's a "composition function". All you do is put the second function in the first. So substitute g(x) for the x in f(x), and you've got your new function. Here are two methods:
1. Find g(2) first, then plug that in to f(x):
g(2)=2(2)+1=5
Plug that into f(x): f(5)=5+4=9.
or
2. Find f@g(x) then plug 2 in for x:
f@g(x)=f(g(x))=f(2x+1)
Plugging (2x+1) in for x gives us
f(2x+1)=(2x+1)+4=2x+5
and
If f@g(x)=2x+ 5, then f@g(2)=2(2)+5=9

The second way looks longer, but they're both handy to know. Hope this helps, and have fun!