Question

suppose that the functions f and g are defined as followsf(x) =-2x^2+3xg(x)=7x-2find (g/f)(-2)

Answer 1

f(x) =-2x^2+3x

g(x)=7x-2

find (g/f)(-2)​

we know that

$\mleft(g/f\mright)\mleft(-2\mright)​=\frac{g(-2)}{f(-2)}$

step 1

Find f(-2)

$\begin{gathered} f(-2)=-2(-2^2)+3\cdot(-2) \\ f(-2)=-8-6 \\ f(-2)=-14 \end{gathered}$

step 2

Find g(-2)

$\begin{gathered} g(-2)=7(-2)-2 \\ g(-2)=-16 \end{gathered}$

step 3

Divide both results

$(g/f)(-2)​=\frac{g(-2)}{f(-2)}=\frac{-16}{-14}=\frac{8}{7}$

therefore

the answer is 8/7