Inverse Function Types

There are various types of inverse functions for common functions, some of these types are discussed as follows:

Inverse Trigonometric Function

Inverse Trigonometric Functions are the inverse functions of the trigonometric ratios, and the table for the range and domain of all the Inverse Trigonometric Functions is as follows:

Exponential and Logarithm Function

Another example of inverse pair is the exponential and logarithm function, both are inverse of each other. For an exponential function f(x) = a^x, its inverse is given by logarithm i.e., log_ax, and vice versa.

Inverse Hyperbolic Function

Similar to the Inverse Trigonometric Function, there are inverse hyperbolic functions, which are the inverse of the hyperbolic trigonometric function i.e., sinh x, cosh x, tanh x, and so on. Inverse Hyperbolic Function are sinh^-1, cosh^-1x, tanh^-1x, cosech^-1x, coth^-1x, and sech^-1x.

Inverse Functions are an important concept in mathematics. To comprehend inverse functions, we can picture a function as a box that takes in inputs and produces outputs. If a function consistently generates a red-colored object as output for any input object, we can identify that box as the initial function. The box that accepts both red and normal-colored objects as inputs and generates the original-colored objects as outputs, is called the inverse of the initial box.

In other words, if a function is an operation that produces an output for each input, the inverse function facilitates the identification of the specific input based on a given output. Let’s learn about inverse functions and all the different associated topics with them.