Question

Hello! I need some help with this homework question, please? The question is posted in the image below. Q1

Answer 1

$\begin{gathered} f(x)=4x+9 \\ g(x)=8x-3 \end{gathered}$

(a)

$\begin{gathered} (f+g)(x)=f(x)+g(x)=(4x+9)+(8x-3) \\ so\colon \\ (f+g)(x)=12x+6 \end{gathered}$

(b)

$\begin{gathered} (f-g)(x)=f(x)-g(x)=(4x+9)-(8x-3)=4x+9-8x+3 \\ so\colon \\ (f-g)(x)=-4x+12 \end{gathered}$

(c)

$\begin{gathered} (f\cdot g)(x)=f(x)\cdot g(x)=(4x+9)(8x-3)=32x^2-12x+72x-27 \\ so\colon \\ (f\cdot g)(x)=32x^2+60x-27 \end{gathered}$

(d)

$(\frac{f}{g})(x)=\frac{f(x)}{g(x)}=\frac{4x+9}{8x-3}$