Inverse Function Calculator

Inverse Function Calculator

Inverse function calculator is used to calculate the inverse of the given function. This inverse of a function calculator provides the step-by-step solution to the given function.

What is an Inverse Function?

A function that "undo" the result of another function is called an inverse function. In other words, if g is a function that "reverses" the impact of g, mapping each element of set X to a distinct element of set Y, then h is said to be the inverse function of g.

 

Let g: A → B be a function more formally. H is the inverse function of g if there is a function h: B A such that h(g(x)) = x for all x in A and g(h(y)) = y for all y in B. Applying f and then g (or g and then f) produces the identity function.

How can we find the inverse of a function?

To find the inverse of a function we have to follow some steps.

• Put the given function equal to y.
• Separate the domain variable for the function.
• In the last change the name of the variable involved in the inverse.

Pictorial Representation:

Let two sets A and B. One set contains elements {x, y,z}, and the other is {1,2,3}. A to B is a function, meaning every element of A has a unique image in set B. For inverse, the given function must be a one-to-one function.

A one-to-one function means all element has a unique and separate image in the 2^nd set. g is the function then the inverse is g^-1.

Pathway to find the inverse function

For the purpose to get the solution, we have to understand this with the help of a numerical example.

Example:

Find the inverse of the function g(x) = 2x + 18.

Solution:

Step 1: First we have replaced g(x) with y from the definition of the function y = g(x)

y = 2x + 18

Step 2: Now separate the variable x.

y – 18 = 2x

x = (y - 18) / 2

Step 3: g(x) = y then x = g-1(y)     

g^-1(y) = (y - 18) / 2

Step 4: Now change the name of the variable from y to x. because the function is independent of the variable name.

g^-1(x) = (x - 18) / 2