Theorem of continuity and limits converge

[Satyr]

Homework Statement

If lim x--> a of [f(x) + g(x)]=2 and lim x--> a of [f(x) - g(x)] = 1, then find lim x--> a f(x)g(x)

Homework Equations

Theorems of continuity

The Attempt at a Solution

Since I'm not quite sure if what I began with was right, it didn't yield me any type of a valid answer. But from the theorems of continuity (lim x--> a of f(x)=f(a)), I began with saying lim x-->2 of [f(x)+g(x)]=2 and lim x-->1 of [f(x)-g(x)]=1

is that a good place to start? where do I go from here?
thanks

 

[Dick]

You mean continuity of f and g tells you f(a)+g(a)=2 and f(a)-g(a)=1, right? That's two equations in two unknowns. You should be able to solve for f(a) and g(a).

 

[Satyr]

right, I've figured that part
i was wondering where I begin doing that?

thanks

 

[Dick]

Add the two equations together to get an equation for just f(a).