Question

Can someone plz help me?
g(x)=-x^2-1-2x
f(X)=X+f
find : (g-f) (x)

Answer 1

f(x) = what?

(That feels like it has a typo)

Answer 2

Hello, njmaia, if you expect help please don't be silent.
I will proceed with an example, although I am still not clear about you original question. In the example I will show how to find (g-f)(x) in general.

Answer 3

Suppose that you are given the following two functions f(x) and g(x).

\(\large\color{black}{ \displaystyle f(x)=-3x^2+5x-3 }\)
\(\large\color{black}{ \displaystyle g(x)=2x^2+3x-5 }\)


(I will denote what corresponds to what using colors)

\(\large\color{black}{ \displaystyle \color{red}{g(x)}-\color{blue}{f(x)}\quad\Longrightarrow \quad \color{red}{\left(2x^2+3x-5 \right)}-\color{blue}{\left(-3x^2+5x-3 \right)} }\)

You know that when you expand parenthesis with a negative inside all terms will change sign (because you are multiplying each term by -1).

\(\large\color{black}{ \displaystyle -\color{blue}{\left(-3x^2+5x-3 \right)}=~+3x^2-5x+3 }\)

Therefore, we can simplify the subtraction:

\(\large\color{black}{ \displaystyle g(x)-f(x)=2x^2+3x-5+3x^2-5x+3 }\)

I colored all like terms, to do the subtraction/addition:

\(\large\color{black}{ \displaystyle g(x)-f(x)=\color{green}{2x^2}\color{darkgoldenrod}{+3x}\color{magenta}{-5}\color{green}{+3x^2}\color{darkgoldenrod}{-5x}\color{magenta}{+3} }\)

\(\large\color{black}{ \displaystyle g(x)-f(x)=\color{green}{2x^2}\color{green}{+3x^2}\color{darkgoldenrod}{+3x}\color{darkgoldenrod}{-5x}\color{magenta}{-5}\color{magenta}{+3} }\)

\(\large\color{black}{ \displaystyle g(x)-f(x)=\color{green}{5x^2}\color{darkgoldenrod}{-2x}\color{magenta}{-2} }\)

And therfore you get:

\(\large\color{black}{ \displaystyle (g-f)(x)= g(x)-f(x)=\color{green}{5x^2}\color{darkgoldenrod}{-2x}\color{magenta}{-2} }\)