Question

f(x) = Square root of quantity x plus nine.; g(x) = 8x - 13

Find f(g(x)).

A. f(g(x)) = 2Square root of quantity two x minus one.
B. f(g(x)) = 8Square root of quantity x minus four.
C. f(g(x)) = 2Square root of quantity two x plus one.
D. f(g(x)) = 8Square root of quantity x plus nine. - 13

Answer 1

@zepdrix

Answer 2

AHHHH quiet down kellbell >.< too loud!

Anyway, so we've got some stuff listed,\[\large\rm f=\sqrt{x+9}\qquad\qquad\qquad g=8x-13\]Our problem is asking us to find the composition, g inside of f.\[\large\rm f(g)=\sqrt{g+9}\]So we take the entire function g, and replace it with every x in f.

Answer 3

lol! sorry, this is just so confusing to me. I will try my best though..

Answer 4

\[\large\rm f=\sqrt{\color{orangered}{x}+9}\]When we take a composition,
we replace all of the x with an `entire function`.\[\large\rm f(\color{orangered}{g})=\sqrt{\color{orangered}{g}+9}\]On the right side of the equals let's plug in our g, ya?\[\large\rm f(\color{orangered}{g})=\sqrt{\color{orangered}{8x-13}+9}\]Confusing?
What do you think KellySpaghetti?

Answer 5

it would be f(g)= sqrt 8g minus 13 + 9, right?..

Answer 6

No no :O I already put the g inside.
Don't put g inside of the g.
That's crazy talk.

Answer 7

oh goodness lol okay

Answer 8

We started with f.
We plugged the letter g in place of x.
We then replaced that g with its equation.
Now simplify from that point,\[\large\rm f(\color{orangered}{g})=\sqrt{\color{orangered}{8x-13}+9}\]

Answer 9

No more fancy plugging.
Just simplify.

Answer 10

this might take me a while lol

Answer 11

Your hair is ridiculous kelly -_- I'm telling your mom

Answer 12

Just combine -13 and 9.
And then we'll have one tiny step after that :)

Answer 13

negative 4 and nooooo don't tell her </3

Answer 14

\[\large\rm f(g)=\sqrt{8x-4}\]Ok great.
These terms have something in common that we can factor out.

Answer 15

4 goes into both of them? or is it 2 that goes into both of them?

Answer 16

4 seems good

Answer 17

awesomesauce

Answer 18

would the answer be D?

Answer 19

hellow?..

Answer 20

Oh sorry you were taking a little while so I went and made a sandwich :D and then read a book :D and watched a full length movie.

Answer 21

nice! what movie?

Answer 22

LOL I was just kidding :D

Answer 23

So you pull the 4 out of each value,\[\large\rm f(g)=\sqrt{4(2x-1)}\]

Answer 24

Then you pull the 4 out of the root because it's a perfect square,
\(\large\rm \sqrt4=?\)

Answer 25

2

Answer 26

\[\large\rm f(g)=\sqrt{4(2x-1)}\]Ok good so it comes out as a 2,\[\large\rm f(g)=2\sqrt{(2x-1)}\]

Answer 27

yay!! thank you!! I have 4 other ones, but I don't think it's fair to keep you from helping everyone else.

Answer 28

If you have other ones that you're stuck on,
open them in a new thread.

I'll try to stop by when I have some spare time :P
Gotta eats mah sammich right now

Answer 29

So it ended up being option A, right?
Yayyy team

Answer 30

yay! and yes :)