Exponential Notation For Function Names
Placing an integer superscript after the name or symbol of a function, as if the function were being raised to a power, commonly refers to repeated function composition rather than repeated multiplication. Thus f 3(x) may mean f(f(f(x))); in particular, f β1(x) usually denotes the inverse function of f. Iterated functions are of interest in the study of fractals and dynamical systems. Babbage was the first to study the problem of finding a functional square root f 1/2(x).
However, for historical reasons, a special syntax applies to the trigonometric functions: a positive exponent applied to the function's abbreviation means that the result is raised to that power, while an exponent of β1 denotes the inverse function. That is, sin2x is just a shorthand way to write (sin x)2 without using parentheses, whereas sinβ1x refers to the inverse function of the sine, also called arcsin x. There is no need for a shorthand for the reciprocals of trigonometric functions since each has its own name and abbreviation; for example, 1/(sin x) = (sin x)β1 = csc x. A similar convention applies to logarithms, where log2x usually means (log x)2, not log log x.
Read more about this topic: Complex Numbers Exponential
Famous quotes containing the words function and/or names:
“It is the function of vice to keep virtue within reasonable bounds.”
—Samuel Butler (18351902)
“The names of those who in their lives fought for life,
Who wore at their hearts the fires centre.
Born of the sun they traveled a short while towards the sun,
And left the vivid air signed with their honour.”
—Stephen Spender (19091995)