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)​=(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)​=(g(-2))/(f(-2))=(-16)/(-14)=(8)/(7)`

therefore

the answer is 8/7