# Thread: probem with function

1. ## probem with function

If f(x)= Log(1+x)/(1-x)
and g(x)= Log(3x+x^3)/(1+3x^2)
then f(g(x))=??
the answer is given in the form of f(x)
HINT if this helps answer is 3f(x)

Pls help me with this thanks

2. $f(x)=log \left( \frac{1+x}{1-x} \right)$

$g(x)=log\left( \frac{3x+x^3}{1+3x^2} \right)$

$f (g(x))=log \left( \frac{1+g(x)}{1-g(x)} \right)$

$f(g(x))=log \left( \frac{1+log\left( \frac{3x+x^3}{1+3x^2} \right)}{1-log\left( \frac{3x+x^3}{1+3x^2} \right)} \right)$

From here it should just be a lot of algebra.

3. Originally Posted by Showcase_22
$f(x)=log \left( \frac{1+x}{1-x} \right)$

$g(x)=log\left( \frac{3x+x^3}{1+3x^2} \right)$

$f (g(x))=log \left( \frac{1+g(x)}{1-g(x)} \right)$

$f(g(x))=log \left( \frac{1+log\left( \frac{3x+x^3}{1+3x^2} \right)}{1-log\left( \frac{3x+x^3}{1+3x^2} \right)} \right)$

From here it should just be a lot of algebra.
Lolz I knw it till here how to proceed next ??

4. Originally Posted by cnpranav
Lolz I knw it till here how to proceed next ??
If you knew it to there then you should have posted that fact so that time and effort was not wasted showing you what you could already do.

I do not see how you can get the so-called answer of $3 f(x)$ from all this. Unless the question asks for a specific form for the answer to be given in, the question has been answered in post #2.

5. Originally Posted by mr fantastic
If you knew it to there then you should have posted that fact so that time and effort was not wasted showing you what you could already do.

I do not see how you can get the so-called answer of $3 f(x)$ from all this. Unless the question asks for a specific form for the answer to be given in, the question has been answered in post #2.
BUt then there is got to be a way to solve the equation??
Or is this the end??

6. There is no "equation" to "solve".

You were asked to compose the functions, and probably then to simplify the resulting expression. That's all.