Question

if f(x) = x/1+x and g(x)= sin 3x what is f(g(x)) and what is its domain

Answer 1

Do you understand how to find the composite?

Basically, you are exchanging g(x) for every X in the F(x)
domain is where the denominator is equal to zero

Post the composite and we can go from there

Answer 2

that is what I thought so I had f(g(x)) = sin3x/1+sin3x but when I plugged that into my homework it said that it was incorrect

Answer 3

Was the problem presented like this: \(\Large\rm f(x)=\dfrac{x}{1+x}\)

or like this: \(\Large\rm f(x)=\dfrac{x}{1}+x\)

I'm assuming it was the first one.
Your solution looks correct, you probably just need to format it properly.

f(g(x)) = sin(3x)/(1+sin(3x))

Answer 4

Your answer is correct, but I think they are requiring parenthesis...you should put what is in the denominator in parenthesis...it can be read a couple of ways...see example above

Answer 5

okay thank y'all very much!

Answer 6

@zepdrix the first way for f(x) is correct but then how would I go about figuring out f(f(x))

Answer 7

\[\Large\rm f(\color{royalblue}{x})=\frac{\color{royalblue}{x}}{1+\color{royalblue}{x}}\]So we're going to take our entire f(x) and plug it in for our x's.\[\Large\rm f(\color{royalblue}{f(x)})=\frac{\color{royalblue}{f(x)}}{1+\color{royalblue}{f(x)}}\]

Answer 8

And so on the right side, we'll plug in the equation for our f(x)'s, yes?

Answer 9

yes so you'll have x/1+x all over 1+ (x/1+x)

Answer 10

Mmm yes, good good :)
\[\Large\rm f(\color{royalblue}{f(x)})=\frac{\color{royalblue}{\left(\frac{x}{1+x}\right)}}{1+\color{royalblue}{\left(\frac{x}{1+x}\right)}}\]

Answer 11

Again though if you want to put that into the website, you'll need to use A LOT more brackets lol

Answer 12

Might be worth your time to simplify first though.

Answer 13

and to simplify I would multiply the top and bottom by (1-x)?

Answer 14

It will work out better to multiply top and bottom by (1+x)

Answer 15

\[\Large\rm f(\color{royalblue}{f(x)})=\frac{\color{royalblue}{\left(\frac{x}{1+x}\right)}}{1+\color{royalblue}{\left(\frac{x}{1+x}\right)}}\color{orangered}{\left(\frac{\left(\frac{1+x}{1}\right)}{\left(\frac{1+x}{1}\right)}\right)}\]You can multiplying it like this, if that helps to see how the fractions will multiply out.
That is the same as multiplying top and bottom by (1+x)

Answer 16

@zepdrix what would the domain be?