Question

Find (ƒ – g)(x) where ƒ(x) = –x2, g(x) = –(x + 4)2.

Answer 1

Given: The functions below

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

To Determine:

`(f-g)(x)`

Solution

`(f-g)(x)=f(x)-g(x)`
`\begin{gathered} =-x^2-(-(x+4)^2) \\ =-x^2+(x+4)^2 \\ =-x^2-(x^2+8x+16) \\ =-x^2-x^2-8x-16 \\ =-2x^2-8x-16 \end{gathered}`

Hence

`(f-g)(x)=-2x^2-8x-16`