anonymous
  • anonymous
Can someone plz help me? g(x)=-x^2-1-2x f(X)=X+f find : (g-f) (x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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SolomonZelman
  • SolomonZelman
f(x) = what? (That feels like it has a typo)
SolomonZelman
  • SolomonZelman
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.
SolomonZelman
  • SolomonZelman
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: \(\large\color{black}{ \displaystyle (g-f)(x)= g(x)-f(x)=\color{green}{5x^2}\color{darkgoldenrod}{-2x}\color{magenta}{-2} }\)

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