The [tex](f-g)(x)=-x^{2} +3x+7[/tex]
We have given that
f(x) = 3x + 1 and g(x) = x² - 6
We have to find (f-g)(x)=?
Now we have (f - g)(x) = f(x) - g(x) ....(by using distributive property for addition)
What is the distributive property?
(a+b)(x)=ax+bx
Therefore we get,
[tex]= 3x + 1 - (x^2 - 6)\\\\= 3x + 1 - x^2 + 6...(Simplify parenthesis)\\\\= -x^2+ 3x + 7.....(Add like terms)[/tex]
Therefore we get the answer is [tex](f-g)(x)=-x^{2} +3x+7[/tex]
To learn more about the subtraction of function visit:
https://brainly.com/question/24380382
