To find the inverse of a function, you reverse the dependent and independent variables and use inverse operations, such as turning an exponential function into a natural logarithm or undoing a square with a square root.
Finding the inverse of a function entails switching the roles of the dependent and independent variables. For example, if the original function is y = f(x), the inverse function would be x = f-1(y). The process of finding an inverse often requires using functions that naturally "undo" each other, such as exponential and logarithmic functions.
Specifically, the exponential function ex is undone by the natural log (ln x), and the base-10 function 10x is undone by the base-10 log (log10 x). In the context of equations, we might have to invert operations such as squaring a value by taking the square root to find the original number. Similarly, an even function y(x) is symmetrical about the y-axis, while an odd function, also known as an anti-symmetric function, is symmetric about the origin, implying reflections over both the x and y-axes.