If h(x) is the inverse of f(x), what is the value of h(f(x))?

by

To understand the expression h(f(x)) when h(x) is the inverse of f(x), we need to delve into the definitions of inverse functions.

An inverse function essentially ‘reverses’ the effect of the original function. Specifically, if y = f(x), then we can say that x = h(y), where h is the inverse of f.

Now, let’s break down the expression h(f(x)):

  1. Start with f(x). This gives you a value, let’s call it y, so y = f(x).
  2. Next, since h is the inverse of f, applying h to y will effectively give you back x.

So, when you compute h(f(x)), it simplifies to:

h(f(x)) = h(y) = x.

In conclusion, if h(x) is indeed the inverse of f(x), then the value of h(f(x)) is simply x. This illustrates the fundamental property of inverse functions, where they essentially ‘cancel’ each other out.

Leave a Comment