Question

how do i find (f/g)(x) for each f(x) and g(x)

f(x)=x / (x+1)
g(x)= (x^2)-1

Answer 1

Well basically you take all of f(x) and put it over g(x) and simplify

Answer 2

\[\Large \frac{\frac{x}{x+1}}{x^2-1}\]

Answer 3

You know how to divide two fractions and simplify, correct?

Answer 4

to find (f/g)(x)..put the value of g(x) at the place of every x in f(x) and similarly to find g(f(x) put the value of f(x) at the place of every x in g(x)

Answer 5

Actually this is asking for (f/g)(x) not f(g(x)) or g(f(x)), this is similar to (f+g)(x) where you would just add the two functions together, but not replace every x value with one function and place it in the other

f(g(x)) or g(f(x)) is not the same method as (f+g)(x) (f-g)(x) (f/g)(x) and (fg)(x)

Answer 6

you got this?

Answer 7

no

Answer 8

i thought that might be the case
lets go slow

Answer 9

ok thanks

Answer 10

\[f(x)=\frac{x}{x+1}\\
g(x)=x^2-1\]right?

Answer 11

that makes
\[\frac{f(x)}{g(x)}=\frac{\frac{x}{x+1}}{x^2-1}\] as a first step, i..e put \(f\) on top of \(g\)
ok with that?

Answer 12

then do write it as one fraction, just like with numbers, put the denominators in the denominator and get
\[\frac{f(x)}{g(x)}=\frac{x}{(x+1)(x^2-1)}\]

Answer 13

and that is finished

Answer 14

oh wow, that didnt look hard as i thought it would be. thank you for your help sir!

Answer 15

yw (sir, i like that...)

Answer 16

:D