Question

.

Answer 1

what is \(f(1)\)?

Answer 2

g(f(1))

Answer 3

but what is f(1)?

Answer 4

-4x + 7?

Answer 5

do you understand what \(f(1)\) means?

Answer 6

it means put a \(1\) in the function \(f\) where ever you see an \(x\).

Answer 7

no this is in a packet about composition of functions. Just problems to work out. I'm trying to look online.

Answer 8

not much explaination

Answer 9

but before you can understand composition of functions, you must understand a function.

Answer 10

okay

Answer 11

for the function \(f(x) = -4x+7\) we have \(f(1) = -4*1+7=3\).

Does this make sense?

Answer 12

yeah

Answer 13

ok now then, what is \(g(3)\)?

Answer 14

g(3) is we put a 3 in the function where the x is @zzr0ck3r

Answer 15

and it would look like g(3) = 2*3 - 6 I think?

Answer 16

which is 0

Answer 17

Hey, so the notation just implies g(f(1)) it's probably simpler to find g(f(x)) first this just means plug the function f(x) wherever there is an x in function g(x). Try that out :)

Answer 18

Or we can do it the way @zzr0ck3r what ever you are comfortable with!

Answer 19

i'm not sure how I would right that

Answer 20

write*

Answer 21

No worries, f(x) = -4x+7 and g(x) = 2x-6 so we take function f(x) and plug it in g(x) \[g(f(x)) = 2(-4x+7)-6\]

Answer 22

Now you can find g(f(1)) by plugging in 1 where the x is and evaluating

Answer 23

Does this make sense? It can be a bit confusing haha.

Answer 24

so it would be 0 then?

Answer 25

It makes sense though a bit complicated. It's something I'm gonna have to really ingrain in my head.

Answer 26

@Astrophysics how would I solve it the way @zzr0ck3r did it? I wasn't sure what to do after he left.

Answer 27

Yup, 0 sounds good!

Answer 28

Thanks for helping me. You're awesome :)

Answer 29

Ok so with zz's method you found what f(1) was which is 3 correct

Answer 30

Then we just take f(1) and plug that in g(x) for g(f(1)) = 2(3)-6 = 0 :)

Answer 31

Either way works :P

Answer 32

oh I see. Both of you guys gave me good ways. Thank you again

Answer 33

Yw :)