# Given F(x) = 3x+1, G(x) = 2x, H(x) = x^2, how do you find the rule for (F o (G o H) )(x)?

Dec 14, 2017

The answer is $= 6 {x}^{2} + 1$

#### Explanation:

The functions are

$f \left(x\right) = 3 x + 1$

$g \left(x\right) = 2 x$

$h \left(x\right) = {x}^{2}$

$\left(g o h\right) \left(x\right) = g \left(h \left(x\right)\right) = g \left({x}^{2}\right) = 2 {x}^{2}$

Therefore,

$f o \left(g o h\right) \left(x\right) = f \left(g \left(h \left(x\right)\right)\right) = f \left(g \left({x}^{2}\right)\right) = f \left(2 {x}^{2}\right) = 3 \left(2 {x}^{2}\right) + 1$

$= 6 {x}^{2} + 1$