if (c(x)=4x - 2) and (d(x)=x^{2}+5x), what is ((ccirc d)(x))?\n(4x^{3}+18x^{2}-10x)\n(x^{2}+9x…

if (c(x)=4x - 2) and (d(x)=x^{2}+5x), what is ((ccirc d)(x))?\n(4x^{3}+18x^{2}-10x)\n(x^{2}+9x - 2)\n(16x^{2}+4x - 6)\n(4x^{2}+20x - 2)

if (c(x)=4x - 2) and (d(x)=x^{2}+5x), what is ((ccirc d)(x))?\n(4x^{3}+18x^{2}-10x)\n(x^{2}+9x - 2)\n(16x^{2}+4x - 6)\n(4x^{2}+20x - 2)

Answer

Explanation:

Step1: Recall composition of functions

The composition $(c\circ d)(x)=c(d(x))$.

Step2: Substitute $d(x)$ into $c(x)$

Since $c(x) = 4x - 2$ and $d(x)=x^{2}+5x$, then $c(d(x))=4(x^{2}+5x)-2$.

Step3: Distribute the 4

$4(x^{2}+5x)-2=4x^{2}+20x - 2$.

Answer:

$4x^{2}+20x - 2$