If f[g(x)] = x, then f(x) and g(x) are inverses of each other.

Why? I don't get this in my math question.

To understand why f(x) and g(x) are inverses of each other if f[g(x)] = x, we need to first discuss what it means for two functions to be inverses.

Two functions, f(x) and g(x), are inverses of each other if and only if applying one function followed by the other results in the original input value, no matter what the input is.

Now, let's see how this applies to the given equation f[g(x)] = x. According to this equation, we start with an input value x and apply g(x) first, then apply f(x) to the result. The equation states that this sequence of operations should always yield the original input value x.

If we assume that g(x) and f(x) are inverses, we can draw the following conclusions:

1. Applying g(x) to x gives us a result, let's call it z: g(x) = z.
2. Applying f(x) to z gives us the original input, x: f(z) = x.

Therefore, if f(g(x)) = x is true, it means that applying g(x) first, followed by f(x), always results in the original input value x. Hence, f(x) and g(x) are inverses of each other.

In summary, the equation f[g(x)] = x is indicative of the fact that f(x) and g(x) are inverses, as it shows that applying g(x) followed by f(x) returns the original input value.