Question

Find (f of g)(x) when f(x)=(√x+3)/x and g(x)=(√x+3)/2x

I know the answer is (f of g)(x)= (x+3)/(2x^2), I just need the steps for it, I'm doing corrections and I can't seem to do it! I know it looks hard, but if you know Pre-Calculus or know someone who does, pleeeeease help!

Answer 1

first off \[f(x)=\frac{\sqrt{x+3}}{x}\]?

Answer 2

yep

Answer 3

ok and is g the same??

Answer 4

The same except for the denominator. The denominator is 2x, rather than x

Answer 5

ok
this is easy to explain using cut and paste

Answer 6

It's frustrating, because I know how to plug it in, the equation just seems impossible to simplify once I do. There's so many square roots.

Answer 7

\[(f\circ )g(x)=f(g(x))\] is always the first step

Answer 8

Yep. And you plug in the G(x) equation for all the x's in the f(x) equation

Answer 9

typo there \[(f\circ g)(x)=f(g(x))\]

Answer 10

right so this is how i do it when i type here
i write \[f(g(x))=f(\frac{\sqrt{x+3}}{2x}) \]as step one

Answer 11

wait not quite. The denominator of F(x) is just x. The denominator of g(x) is 2x.

Answer 12

well step two actually but whatever
then since \[f(\heartsuit)=\frac{\sqrt{\heartsuit}}{\heartsuit}\] i copy and past \(\frac{\sqrt{x+3}}{2x}\) in for the \(\heartsuit\)

Answer 13

ok
yeah I've done that. After that I don't know what to do
to simplify

Answer 14

oops another typo \[f(\heartsuit)=\frac{\sqrt{\heartsuit+3}}{\heartsuit}\]

Answer 15

ok let me copy and paste, see what we get

Answer 16

Btw thank you so much most people don't like answering advanced level questions on here!!

Answer 17

\[f(\heartsuit)=\frac{\sqrt{\heartsuit+3}}{\heartsuit}\]
\[f(\frac{\sqrt{x+3}}{2x})=\frac{\sqrt{\frac{\sqrt{x+3}}{2x}+3}}{\frac{\sqrt{x+3}}{2x}}\]

Answer 18

@whovianchick Some people prefer to answer advanced questions on here :P

Answer 19

Yep. I've got that equation on my paper. It sucks butt.

Answer 20

hmm how this is going to end up as what you wrote is anyones guess
in fact i think it will not, because of the nested radical
is there perhaps a typo?

Answer 21

dividing by a fraction is the same as multiplying by the reciprocal so we can start with that

Answer 22

Here let me get a screenshot of the question

Answer 23

that is a good idea

Answer 24

ta-daaaaaa

Answer 25

lol

Answer 26

that is a times sign, not a circle for composition
you are working too hard
just multiply

Answer 27

wat

Answer 28

DANGIT

Answer 29

it is times, not compose
do it in your head

Answer 30

IT LOOKS THE EXACT SAME IN THIS CURRICULUM

Answer 31

\[\circ \]\[\cdot\]

Answer 32

Lol. Well thank you. That was more help than I ever could've asked for. I'm gonna try to work it on my own, I'll tag you if I get lost again, but for both our sakes, I hope I don't lol

Answer 33

no prob

Answer 34

Well, I solved the case in record time. I also put on my readers.