learning journal unit4.docx - An inverse function does the...

An inverse function does the exact opposite, undoing what the original function
does. It is usually denoted as f
-1
(x), and it reverses the f(x) processes. Before a function
can have an inverse, it must first be one-to-one; that is, it must pass the horizontal line
test, which verifies whether a function is one-to-one by intersecting the function's graph
only at one point. The graph of f -1 (x) on a set of axes can be obtained by reflecting our
original function on a diagonal line y = x which is called identity line ( Abramson, 2017, p.
262) . Importantly, one must note that not all functions have an inverse function .
The function f(x) can be reversed in such a way that the input of the function becomes
the output and the output becomes an input, and the resulting reversed relationship is
itself a function f
-1
(x) , then f
-1
(x) is the inverse of f(x) .
The definition of the inverse of a function state that, the domain of f(x) is equal to the range
of f -1 (x) and vice versa. This means that, if the function f (x) is the set of ordered pairs (x, y),
then the inverse of f(x) is the set of ordered pairs (y, x) and when the function is defined by an