Question

F(x)=2x^2-x-6 g(x)=4-x (f+g)(x)

Answer 1

`\large \boxed{(f + g)(x) = f(x) + g(x)}`

The property above is distribution property where we distribute x-term in the function.

Substitute both f(x) and g(x) in.

`\large{ \begin{cases} f(x) = 2 {x}^(2) - x - 6 \\ g(x) = 4 - x \end{cases}} \\ \large{f(x) + g(x) = (2 {x}^(2) - x - 6) + (4 - x)} \\ \large{f(x) + g(x) = 2 {x}^(2) - x - 6 + 4 - x}`

Évaluate/Combine like terms.

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

The function can be factored so there are two answers. (Both of them work as one of them is factored form while the other one is not.)

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

Alternative

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

Answer

• (f+g)(x) = 2x²-2x-2
• (f+g)(x) = 2(x²-x-1)

Both answers work. The second answer is in factored form.

Let me know if you have any doubts!