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 (Headbang)

Printable View

- Apr 9th 2009, 11:28 PMcnpranavprobem 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 (Headbang) - Apr 10th 2009, 02:18 AMShowcase_22
$\displaystyle f(x)=log \left( \frac{1+x}{1-x} \right)$

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

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

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

From here it should just be a lot of algebra. - Apr 10th 2009, 04:21 AMcnpranav
- Apr 10th 2009, 04:43 AMmr 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 $\displaystyle 3 f(x)$ 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. - Apr 10th 2009, 04:48 AMcnpranav
- Apr 10th 2009, 05:01 AMstapel
There is no "equation" to "solve". (Wondering)

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