Final answer:
Composing inverse functions results in the identity function, as inverse functions are designed to counteract each other. An example is applying an exponential function to a number followed by a natural logarithm, leading back to the original number.
Step-by-step explanation:
When you compose inverse functions, the result is the identity function. This is because inverse functions are designed to 'undo' each other. For instance, if you take a number and apply an exponential function and then apply the natural logarithm to the result, you would return to the original number because the natural logarithm is the inverse of the exponential function. This property holds for all inverse pairs, such as sine and arcsine, or square functions and square root functions.
Analogous to the dimensional consistency in equations, where the expressions on both sides must have the same dimensions, when we compose one function with its inverse, we must end up with the same quantity we started with. Like any fraction with the same quantity in the numerator and the denominator (which equals one), the composition of a function and its inverse equals the identity function, returning the original input.