Question

O GRAPHS AND FUNCTIONSSum, difference, and product of two functions

Answer 1

Given: The functions below

$\begin{gathered} f(x)=2x^2 \\ g(x)=x^3 \end{gathered}$

To Determine: The following

$\begin{gathered} a)(fg)(x) \\ b)(f-g)(x) \\ c)\cdot f+g)(-2) \end{gathered}$

Solution

$\begin{gathered} (fg)(x)=f(g(x)) \\ f(g(x))=f(x^3) \\ f(x^3)=2(x^3)^2 \\ f(x^3)=2x^{3\times2} \\ f(x^3)=2x^6 \end{gathered}$

Hence,

$(fg)(x)=2x^6$$\begin{gathered} b)(f-g)(x)=f(x)-g(x) \\ f(x)-g(x)=2x^2-x^3 \\ \text{Hence,} \\ (f-g)(x)=2x^2-x^3,or,x^2(2-x) \end{gathered}$$\begin{gathered} c)(f+g)(-2)=f(-2)+g(-2) \\ f(x)=2x^2 \\ f(-2)=2(-2)^2=2(4)=8 \\ g(x)=x^3 \\ g(-2)=(-2)^3=-8 \\ \text{Therefore} \\ f(-2)+g(-2)=8+(-8)=8-8=0 \end{gathered}$

Hence

$(f+g)(-2)=0$

ANSWER SUMMARY

(fg)(x) = 2x⁶

(f-g)(x) = 2x²-x³

(f+g)(-2) = 0