Question

Subtract the given function and indicate the domain of the difference

Answer 1

Answer:

The domain is $x\in (-\infty,\infty).$

Step-by-step explanation:

Given functions $f(x)=x^2+3x+1$ and $g(x)=2x^2-4x-1$

Subtract these two functions:

$f(x)-g(x)\\ \\=(x^2+3x+1)-(2x^2-4x-1)\\ \\=x^2+3x+1-2x^2+4x+1\\ \\=(x^2-2x^2)+(3x+4x)+(1+1)\\ \\=-x^2+7x+2$

Plot these difference on the coordinate plane (see attached diagram). This function is defined for all vlues of x, so the domain is $x\in (-\infty,\infty).$