Question

Find f(x) and g(x) so that the function can be described as y = f(g(x)).

y = 3/sqrt3x+4

Answer 1

\[y=\frac{ 3 }{ \sqrt{3x+4} }\]

Answer 2

@jim_thompson5910 can you help? Please:)

Answer 3

are you given answer choices?

Answer 4

because this question is open-ended (ie there are multiple ways to do this)

Answer 5

off the multiple choices as jim_thompson5910 already pointed out
think about if you were to make
f(x) = 3/x

what will be your g(x)?

Answer 6

f(x) = \[\frac{ 3 }{ \sqrt{x} }\], g(x) = 3x + 4

f(x) =\[\sqrt{3x+4}\] , g(x) = 3

f(x) =\[\frac{ 3 }{ x }\] , g(x) = 3x + 4

f(x) = 3, g(x) = \[\sqrt{3x+4}\]

Answer 7

Sorry thats really hard to read but those are the answer choices

Answer 8

A) f(x) =3/sqrt x , g(x) = 3x + 4

B) f(x) = sqrt 3x+4 , g(x) = 3

C) f(x) = 3/x , g(x) = 3x + 4

D) f(x) = 3, g(x) = sqrt 3x+4

Answer 9

Answer choices!

Answer 10

if you look at choice C, saying f(g(x)) would get you this

f(x) = 3/x

f(g(x)) = 3/(g(x)) ... replace every x with g(x)

f(g(x)) = 3/(3x+4) ... replace every g(x) on the right with 3x+4


so this is close to what we want, but not quite

Answer 11

so C is out

Answer 12

Okay!

Answer 13

see how I got that?

Answer 14

Yes

Answer 15

so what is f(g(x)) for choice B?

Answer 16

\[\sqrt{13}\]

Answer 17

so that's out too because that's not what we want

Answer 18

for choice D, f(x) is always 3, so no matter what you plug in for x, it's going to remain 3

besides, there is no x to replace anyway (on the right side)

so for choice D, f(g(x)) = 3

so D is out

Answer 19

Okay, so the answer is a

Answer 20

yep, I would do the same thing we've been doing to check though (so you get the practice)

Answer 21

okay, Thank you so much!

Answer 22

yw