Question 241965
f(g(x)) means f of (g of x)


f and g are the names of the functions.


x is the name of the variable the functions are working on.


you first find g(x) and then you find f(g(x))


in your problem:


f(x) = x-3


g(x) = x-2


if you want f(g(x)), you do the following;


first you find g(x).


That equals x-2.


Then you find f(g(x)) by replacing g(x) with (x-2) because they are equal.


f(g(x)) becomes f(x-2).


next you take your equation of f(x) = x-3 and you replace x with g(x).


your equation becomes:


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


then you simplify the equation to get:


f(g(x)) = x-5