Question

F(x) = x2 + 1 g(x) = 5 – x

(f + g)(x) =

Answer 1

`(f + g)(x) = {x}^(2) - x + 6`

Explanation:

We have

`f(x) = {x}^(2) + 1`

and

`g(x) = 5 - x`

We want to find (f+g)(x).

By the algebraic properties of polynomial functions,

`(f + g)(x) = f(x) + g(x)`

`(f + g)(x) = {x}^(2) + 1 + 5 - x`

This simplifies to

`(f + g)(x) = {x}^(2) - x + 6`

We can't simplify further, hence the simplest form