Question

Express the following function, F(x), as a compisition of two functions, f and g. f(g(x)). F(x) = square root of 3x-4. Picture of the question is attached :O

Answer 1

Well i can tell you that g(x) is 3x-4.
Now why?
Well composition functions mean one function INSIDE of another function. So there you simply have two functions. YOure goal is to find them.
The problem tells you that you have f(g(x)) equals F(x) and F(x)= the square root of 3x-2... Now there are two functions in that problem.. f and g. To find them we can simply see that f(x) is the square root of x. and g(x) is 3x-2? why because in this we see that g is inside of f here -> f(g(x)) so here g being 3x-2 is inside of f being square root of x.
Does that make sense?

Answer 2

yes that really does! so if i needed to find f(x) by identifying what i did to the function in part 1, how would i find the function of f(x)?

Answer 3

Its basically what i said in the first one. f(x) is square root of x

Answer 4

well if f(x) is the square root of x would it be f(x)=square root of 3x-4?

Answer 5

you have three functions youre looking at here.. you have F(x).. f(x)... and g(x).. part two is asking for f(x).. the outside part of square root of 3x-2 seen here in f(g(x)) so
f(x)=square root of x
g(x)=3x-2
F(x)=square root of 3x-2

Answer 6

ohh i thought F(x) and f(x) were basically the same thing!

Answer 7

so then the answer to that question is simply "square root of x"?

Answer 8

yep!

Answer 9

awesome! thanks!! i have one last question if you dont mind :o im almost done with this worksheet! :D

Answer 10

how would i answer "verify f(g(x)) = F(x)
f(g(x)) = square root of 3x-4"

Answer 11

This one you have to show work.. Here ill show you...

Answer 12

So to verify that \[f(x)=\sqrt{x} \] and g(x)=3x-2.. We need to plug in f(x) and g(x) into f(g(x)) because the problem says that F(x)=f(g(x))...
Heres how we do it.
f(g(x))=F(x)
f(3x-2)=F(x).... Now here in f for every time we see an x for f(x) we plug in 3x-2.... and f(x) =square root of x... so we get
f(g(x))=square root of 3x-2=F(x) ... Is this true??? Yes so we did it right!

Answer 13

wow that seems so much easier when broken down! so the official answer is just f(g(x))=square root of 3x-2=F(x) ?

Answer 14

are you just saying that? lol or is it really helping? honestly lol. and yeah it is but you have to show all your work since its telling you to verify it meaning to show your work

Answer 15

no lol im serious. i dont have a teacher or textbook and im doing pre cal on an online system so its really hard for me because they dont show us how to do this kind of stuff so it really helps me to see what steps you did to get what because if not i would be totally lost

Answer 16

well thats good im glad to hear that I can help(: Im basically just on this site cause i like to help others. I really should be doing my own homework and stuff but oh well>.< i really enjoy helping people

Answer 17

yes, thank you so much! you have NO idea how much of a difference you're making to me :) people like me definitely appreciate people like you :D i dont know what grade youre in but if theres anything i can help with, let me know :) i would love to be able to pay you back!

Answer 18

awh you're adorable (no im not really flirting dont report me lol you're just really nice and sweet!) and im a senior in highschool. you?

Answer 19

hahaha i wont report you! & thanks, so are you! :) & im a senior in high school also :)

Answer 20

oh look at you you nerd taking an online math class! haha i thought you would be like a freshman in college or something. Well thats good that youre a nerd though! :P

Answer 21

hahah i had a cheerleading accident so since i have to miss like 6 months im just finishing senior year online :p and hahaha i am nerdy ;P but math is definitely my worstttt subject lol