Inverse,Periodicity of Functions

What is a Period?

The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function. In other words, a periodic function is a function that repeats its values after every particular interval.

$$f(x+a)\space = \space f(x) for\space a>0$$

How to find a period?

• If a function repeats over at a constant period we say that is a periodic function.
• It is represented like f(x) = f(x + p), p is the real number and this is the period of the function.
• Period means the time interval between the two occurrences of the wave.

$$If\space for\space f(x)\space period\space =\space T,\space then\space period\space for\space f(ax)\space =\space \frac{T}{a}$$

$$Rest\space for\space all\space other\space cases\space of\space functions,\space the\space period\space remains\space same$$

What are inverse functions?

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x.

If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f^-1- or F^-1.

How to find inverse?

The graph of the inverse of a function reflects two things, one is the function and second is the inverse of the function, over the line y = x.

$$The\space inverse\space function\space returns\space the\space original\space value\space for\space which\space a\space function\space gave\space the\space output.$$