How do I combine f(x) and g(x) to find the limit as x approaches 1?

[fruitbowl]

Homework Statement

Apologies for any trouble, but I'm not going to post any numbers, as my school is very sensitive about plagiarism and the like in homework. I only need some help in figuring out what to do.

I'm given a table of x values 1 to 5, and for each, corresponding y-values for two functions: f(x) and g(x). So my table has three rows x, f(x), and g(x).

I have to find the limit of [2f(x) - 3g(x)] as x approaches 1.

I can do g(f(x)), but... Af(x) - Bg(x)? What...?

I know limits are calculus stuff, but what I really need help with here is manipulating g(x) and f(x), and that should be precalculus... right?

Homework Equations

None that I know of

The Attempt at a Solution

I'm stumped. The first thing that did cross my mind was substituting the y values I'm given from the table into f(x) and g(x), but... that can't be right! I get a number that makes no sense.

 

[ƒ(x)]

I fail to see the problem. [2f(x) - 3g(x)] doesn't involve compound functions.

 

[fruitbowl]

Hmm, so should I just post this in the calculus forum? I just don't know how to find the limit of [2f(x) - 3g(x)] as x approaches 1.

 

[HallsofIvy]

$$\lim_{x\to a} (Af(x)+ Bg(x))= A(\lim_{x\to a} f(x))+ B(\lim_{x\to a} g(x))$$

I would think you would have learned that well before
$$\lim_{x\to a} f(g(x))$$

 

[fruitbowl]

Ah, thank you so much!