Question

if f(x) = 3-2x and g(x) = 1 ÷ x+5 , what is the value of (f/g) (8)

Answer 1

$(\frac{f}{g})(x)=\frac{f(x)}{g(x)}$

so
$(\frac{f}{g})(8)=\frac{f(8)}{g(8)}$

find f(8) and g(8)

f(8)=3-2(8)=3-16=-13
$g(8)=\frac{1}{8+5}=\frac{1}{13}$

so
$\frac{f(8)}{g(8)}=\frac{-13}{\frac{1}{13}}=(-13)(13)=-169$

$(\frac{f}{g})(8)=-169$

Answer 2

$\bf \begin{cases} f(x)=3-2x\\ g(x)=\frac{1}{x+5} \end{cases}\qquad \left( \cfrac{f}{g} \right)(8)\implies \cfrac{f(8)}{g(8)}\implies \cfrac{3-2(8)}{\frac{1}{(8)+5}} \\\\\\ \cfrac{3-16}{\frac{1}{13}}\implies \cfrac{-13}{\frac{1}{13}}\implies \cfrac{\frac{-13}{1}}{\frac{1}{13}}\implies \cfrac{-13}{1}\cdot \cfrac{13}{1}\implies -169$