Question

Subtract the given function and indicate the domain of the difference

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

Answer 1

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

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).`