What is "if h(x) is the inverse of f(x)?

If h(x) is the inverse of f(x), it means that when you compose h with f(x) or f with h(x), you get the identity function. In other words, h(f(x)) = x and f(h(x)) = x for all x in the domain of h and f.

This relationship between h and f implies that they are reflections of each other over the line y = x. This means that the graph of f(x) can be obtained by reflecting the graph of h(x) over the line y = x, and vice versa.

The existence of an inverse function implies that f(x) is a one-to-one function, which means that each output of f(x) corresponds to a unique input, and each input has a unique output. This property is necessary for a function to have an inverse.

To find the inverse function h(x) of f(x), you can switch the roles of x and y in the equation y = f(x) and solve for y to find h(x). The notation for the inverse function is typically denoted as f^(-1)(x) = h(x).