If f(x) = x2 – 2 and g(x)=x-3, what is (fog)(x)?

So first we have to know what (fog)(x) means. Whenever we have the notation (fog)(x) or (gof)(x) or whatever variables (hof)(c) it means that we put the function closest to the x in the other function.

Basically for (fog)(x) this means put g(x) in f(x)

For (hof)(c) this means put f(c) in h(c)

For (gof)(x) this means put f(x) in g(x)

So now we can proceed with the problem.

f(x) = x^2 - 2 (I assume you wrote x squared) and g(x) = x - 3. Find (fog)(x)

So we are going to put g(x) in f(x). So wherever there is an x in f(x) we are gonna replace that with x -3:

f(g(x)) = (x-3)^2 - 2

If we want we can foil this out:

(x-3)(x-3) - 2

x^2 - 6x + 9 -2

or x^2 - 6x + 7

So: (fog)(x) = x^2 - 6x + 7

*If you meant 2x the process is the same but will give you a different answer*