How to find $f(x)$ in the composite function $f(f(x)) = 6x-8$ where f(x) is a linear function Hi just want to know how to solve this. 
find $f(x)$ in the composite function $f\bigl(f(x)\bigr) = 6x-8$

If you consider a linear function $f(x)=mx+b$, we have $f(f(x))=m(mx+b)+b$.
This is equal to $m^2x+mb+b$.
We have that $m^2=6$, so $m=\sqrt{6}$.
Therefore, $\sqrt{6}b+b=8$,
We have $b(\sqrt{6}+1)=8$, so $b=\displaystyle \frac{8}{\sqrt{6}-1}=\frac{8\sqrt{6}+8}{5}$
Therefore, $\displaystyle f(x)=x\sqrt{6}+\frac{8\sqrt{6}+8}{5}$, is a solution.
