Help me figure out this f(x) problem, PLEASE! :)?

Ok, let me explain functions to you.

You've seen an equation like this many times:

y=3x

This equation can also be described as function y in variable x. Notation for this is y(x).

If we solve for x instead to get x=y/3, this can be described as function x in variable y, or x(y).

Now for function y, the original one, we can put anything in for a variable. Example:

y(x) ---> y=3x

y(z) ---> y=3z

y(u+17) ---> y=3(u+17)

y(5) ---> y=3(5)=15

So for notation y(#), y is the function and # (which is whatever is in the parentheses) is what gets substituted for the variable.

So for your problem above, there are actually 2 functions involved: f and g. In f(g(x)), g(x) is in the parentheses for f, so g(x) will be substituted in for the variable for f:

f(g(x)) = f(x^2-2) = 4(x^2-2)+1 = 4x^2-7

Read it over a couple times, you'll get it. Good luck :)