Question

Let f(x) = x + 5 and g(x) = x2. Find (g ͦ f)(6)?
a. 81
b. 36
c. 121
Can you show your work too? I've asked the teacher but I still don't get it and I need to know how. I've tried every math site and my textbook, with the math I tried to do I think it might be 36 but I'm not sure...please help, please I really need the help.

Answer 1

so (g o f)(6)
means g(f(6))
this means we need to start with the inside f(6)
what is f(6)
well f(x)=x+5
so f(6)=6+5=?

Answer 2

after we find f(6)
we will need to find g(f(6))

Answer 3

@Vendela are you there

Answer 4

Yeah I'm listening

Answer 5

well can you tell me what f(6) is?

Answer 6

umm...is it 11,because of the 6+5?

Answer 7

yes
so we have g(f(6))=g(11)

Answer 8

but g(x)=x^2

Answer 9

so g(11)=?

Answer 10

66?

Answer 11

11^2 isn't 66

Answer 12

oh whoops wrong number lol okay it'd be 121

Answer 13

\[(g ^o f)(6)=g(f(6))=g(6+5)=g(11)=11^2=121 \text{ yes! }\]

Answer 14

OMG thank you soooooooooo much!!!!!!!1

Answer 15

do you want to try to find (f o g)(6)?

Answer 16

*!

Answer 17

oh yes

Answer 18

so that means f(g(6)) right
so this time g(6) is inner most thing to evaluate

Answer 19

g(6) tells us we are going to use the function called g
and g(x)=x^2
so g(6)=?

Answer 20

36

Answer 21

so we have f(g(6))=f(36)

Answer 22

do you know how to evaluate f(36)?

Answer 23

no not really

Answer 24

well isn't f given by f(x)=x+5

Answer 25

okayy

Answer 26

since f(x)=x+5
then f(36)=36+5

Answer 27

41

Answer 28

\[(g ^o f)(6)=g(f(6))=g(6+5)=g(11)=11^2=121 \\ (f ^o g)(6)=f(g(6))=f(6^2)=f(36)=36+5=41\]

Answer 29

now i hope you notice that was just an extra question

Answer 30

so the answer is 121?

Answer 31

just for more practice

Answer 32

yes

Answer 33

you might want to practice these compositions more

Answer 34

Thank you so so so so much.You are honestly better than my math teacher:P how do I medal+fan?

Answer 35

you can medal and fan if you want
but it is not required
the best response button on this post will give me a medal
scrolling over my name will show you a tab to become a fan

Answer 36

awesome!! thank you again!!

Answer 37

np