Hello strigy Originally Posted by
strigy How do I find g(x) if f(x) = x+1/x and f o g(x) = 3x+1?
I've gotten as far as g(x) + 1 = g(x)(3x + 1)
What do I have to do next?
Thanks for the help!
Having read what has been written so far, I wonder if the question is really$\displaystyle f(x) = \frac{x+1}{x}$
If it is, then you're right: $\displaystyle g(x) + 1 = g(x)(3x+1)$. So you can now say:$\displaystyle g(x) + 1 = 3x.g(x)+ g(x)$
$\displaystyle \Rightarrow 3x.g(x) =1$
$\displaystyle \Rightarrow g(x) = \frac{1}{3x}$
You can now check this:$\displaystyle f\circ g(x) = f\left(\frac{1}{3x}\right)$$\displaystyle = \frac{\dfrac{1}{3x}+1}{\dfrac{1}{3x}}$
$\displaystyle =\frac{1+3x}{1}$
$\displaystyle =1+3x$
If $\displaystyle f(x) = x + \frac1x$, then you'll have to do as HoI suggests and use the quadratic formula.
Grandad