Question

For the function `f(x) = 1+3x-x^2`, what is `f(p)+5`?

Answer 1

`f(p)+5=6+3p-p^2`

Write as `-p^2+3p+6`

Explanation:

`f(x) = 1+3x-x^2`
`f(p)=1+3p-p^2`

So `f(p)+5" "=" "1+3p-p^2+5`

`color(white)(f(p))f(p)+5" "=" "6+3p-p^2`

Answer 2

`f(p)+5=color(green)(6+3p-p^2`

Explanation:

Given: `f(color(blue)(x))=1+3color(blue)x-color(blue)x^2`
Then
`color(white)("XXX")f(color(red)p)color(white)("xx")=1+3color(red)(p)-color(red)(p)^2`
and
`color(white)("XXX")f(color(red)p)color(magenta)(+5)=1+3color(red)p-color(red)(p)^2color(magenta)(+5)`

`color(white)("XXXXXXxX")=6+3color(red)p-color(red)p^2`