It helps to first clarify that the notation (f - g)(x) simply means f(x) - g(x). Given that, let's look at our f(x) and our g(x) here, and use their definitions to find their difference.
[tex]f(x)=3x+1\\g(x)=x^2-6[/tex]
When we're taking (f - g)(x), we simply substitute the expression 3x + 1 for f(x) and the expression x² - 6 for g(x) to obtain:
[tex](3x+1)-(x^2-6)=3x+1-x^2+6[/tex]
Or, ordering the polynomial from highest power to lowest and combining the constants:
[tex]-x^2+3x+7[/tex]
Edit: By request, here's what would happen if you had something instead like:
[tex](f\times g)(x)[/tex]
In this case, you'd have to *multiply* the two function expressions together. Here's what that would look like:
[tex](3x+1)(x^2-6)[/tex]
Using the distributive property, we can distribute the expression [tex]3x+1[/tex] to the terms [tex] x^{2} [/tex] and [tex]-6[/tex]:
[tex](3x+1)x^2-(3x+1)6[/tex]
Distributing again, we get:
[tex]3x(x^2)+x^2-3x(6)+6=3x^3+x^2-18x+6[/tex]
And we're done.
