Question

Attached is a photo of my written question, thank you.

Answer 1

Given:

The function is,

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

Step-by-step explanation:

Determine the function for f(x + h).

`\begin{gathered} f(x+h)=-2(x+h)^2-(x+h)+3 \\ =-2(x^2+h^2+2xh)-x-h+3 \\ =-2x^2-2h^2-4xh-x-h+3 \end{gathered}`

Determine the value of expression.

`\begin{gathered} (f(x+h)-f(x))/(h)=(-2x^2-2h^2-4xh-x-h+3-(-2x^2-x+3))/(h) \\ =(-2h^2-4xh-h)/(h) \\ =-2h-4x-1 \end{gathered}`

So exprression after simplification is,

-2h - 4x - 1