# If F(F(x))=16x-4 what is F(x) ?

Nov 19, 2016

$k = - \frac{4}{5} , h = 4$ or $k = \frac{3}{4} , h = - 4$

#### Explanation:

$F \left(F \left(x\right)\right) = h \left(h x + k\right) + k = {h}^{2} x + k \left(h + 1\right)$ but

${h}^{2} x + k \left(h + 1\right) \equiv 16 x - 4$. This relationship must be true for all $x$ so the conditions are

$\left\{\begin{matrix}4 + k + h k = 0 \\ {h}^{2} - 16 = 0\end{matrix}\right.$

Solving for $k , h$ we have

$k = - \frac{4}{5} , h = 4$ or $k = \frac{3}{4} , h = - 4$