The first step in determining whether f(x) and g(x) are inverses of each other is to compose the functions. That is, we have to calculate f(g(x)) and g(f(x)).
Starting with f(g(x)), we replace 'x' in f(x) with the function g(x). So, we have f(g(x))=2-(3/5)[-(5/3)x+(10/3)].
Similarly, for g(f(x)), we replace 'x' in g(x) with the function f(x). Thus, we have g(f(x))=-(5/3)[2-(3/5)x]+(10/3).
After calculating f(g(x)) and g(f(x)), we see that both f(g(x)) and g(f(x)) equal x. However, for two functions to be inverse of each other, f(g(x)) should equal x and also g(f(x)) should equal x.
So, let's compare f(g(x)) to x and also g(f(x)) to x. We find that both f(g(x)) and g(f(x)) are equal to 'x', indicating that the two functions are not inverses of each other.
Therefore, the first step in determining if f(x) and g(x) are inverses is to compose the functions f(g(x)) and g(f(x)) and comparing to 'x'. If both f(g(x)) and g(f(x)) equal to 'x', then the functions are inverses of each other and vice versa. In this case, it is determined that f(x) and g(x) are not inverses of each other.