SAT® Subject Test in Math 1 & 2

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Difficult

Determining a New Function

SATSTM-UNQGNG

The functions $f$ and $g$ are defined by $f(x)={x}^{2}$ and $g(x)=2x$.

Which one of the following is the function $h(x)=\cfrac{f(2x)\cdot g(-2x)}{2}$ in terms of $x$?

A

$-4{x}^{3}$

B

$-8{x}^{3}$

C

$-8{x}^{5}$

D

$-4{x}^{5}$

E

$-16{x}^{3}$