What is an Isarithm in Mathematics?

Isarithm is a term used in mathematics to describe a function that has the same shape as its inverse function. In other words, if we have a function f(x) and its inverse function f^-1(y), then the two functions have the same graph, but with a horizontal reflection.

More formally, if we have a function f(x) such that f(x) = y, then the isarithm of f(x) is the function g(y) such that g(y) = x, where g(y) = f^-1(y). In other words, the isarithm of f(x) is the function that "reverses" the relationship between x and y, so that we can go from y to x and back again.

Here's an example:

Suppose we have a function f(x) = 2x + 3. To find the isarithm of this function, we need to find the inverse function, which is f^-1(y) = (y - 3)/2. The isarithm of f(x) is then g(y) = (y - 3)/2, which is the function that "reverses" the relationship between x and y.

So, if we start with a value of y, we can use the isarithm g(y) to find the corresponding value of x. For example, if we start with y = 4, then g(4) = (4 - 3)/2 = 1, so the value of x that corresponds to y = 4 is x = 1.

I hope this helps! Let me know if you have any other questions.