For f(x)=3x+1 and g(x)=x squared - 6 find (f- g)(x)

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.



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:



Or, ordering the polynomial from highest power to lowest and combining the constants:



Edit: By request, here's what would happen if you had something instead like:



In this case, you'd have to *multiply* the two function expressions together. Here's what that would look like:



Using the distributive property, we can distribute the expression  to the terms  and :



Distributing again, we get:



And we're done.