To determine the value of h(fx), we need to understand the relationship between a function and its inverse.
Given that h is the inverse of f, we know that by definition:
- f(h(x)) = x for all x in the domain of h.
- h(f(x)) = x for all x in the domain of f.
From this definition, when we evaluate h(f(x)), we replace f(x) with its input to the function h. Thus:
h(f(x)) = x
Therefore, for any f(x), applying h results in the original input x. In other words, h(fx) = x indicates that applying the inverse function to the output of the original function returns the input value.
In conclusion, the value of h(fx) is simply:
x