Question

find (fog)(2) and (f+g)(2) when f(x)=1/xand g(x)=4x+9

Answer 1

So we need to find f(g(2)) and we also need to find f(2)+g(2)

Answer 2

do you know how to find g(2)?

Answer 3

do you plug in 2 for the g=4x+9?

Answer 4

you plug in x for 2 in the expression named g
yes

Answer 5

so it equals 17?

Answer 6

g(2) is 17
that is right

Answer 7

so do you know how to find f(g(2))
you just found g(2)
so you need to find f(g(2)) now
f(g(2))=f(17)
I replaced g(2) with 17
now you need to find f(17)
f(g(2))=f(17)=?

Answer 8

so you plug in 17 where the f(x)=1/x right?

Answer 9

right

Answer 10

so f(g(2))=?

Answer 11

1/17?

Answer 12

right

Answer 13

now f(2)+g(2)
you already found g(2) earlier
you said it was 17
so we have
now f(2)+g(2)
f(2)+17

Answer 14

any clue what to do now?

Answer 15

\[\frac{ 1 }{ 17 }+\frac{ 17 }{ 1 }i am assuming\]

Answer 16

how did you get f(2) is 1/17?
I think f(x)=1/x
so f(2)=?

Answer 17

oh my apoligize so is it 1/2

Answer 18

yep
great job
now you need to simplify f(2)+g(2)
f(2)+g(2)
=
1/2+17

Answer 19

guess you could write that as a mix fraction

Answer 20

which basically it is already written that way

Answer 21

anyways lets summarize what we did
we found f(g(2))=1/17
we also found f(2)+g(2)=17+1/2

Answer 22

so do we just plug in 2 where ever there is an x and then we just just combine f and g in (fog) or do we just leave it as (fog)(2) and do we just leave it as 1/2+17 for (f+g)(2)?

Answer 23

i didn't write 17+1/2 as a mix fraction i left that part for you

we were asked to find (f o g)(2) which is f(g(2))
all you do first is take the g function and replace x's with 2's
then take whatever result you get from that in plug into f which I believe we got 1/17 if i remember correctly


by the way (g o f)(2) means g(f(2)) so you would start with f first if you seen this


(f+g)(2) just means f(2)+g(2)

Answer 24

thank you :D