Inverse functions are important in mathematics and can be very useful in real life. In this article, we will discuss what is an inverse function. How to find inverse functions using algebra and their properties. What is an Inverse Function? An inverse function is a type of function that has the same graph as its inverse. In other words, if f(x) is the inverse function of g(x), then g(-x) is the inverse function of f(x).
What are Inverse Functions?
An inverse function is a relation between two functions. It is defined as follows:
if f and g are functions then f(g(x)) = x. This equation implies that if you plug in any number of x, you will get an output of y=x inverted.
Inverse functions can be used to find the inverse function of the given relation by solving the given relation for x or y if it’s already been solved for both variables (in which case it’s easy to check whether they’re equal).
For example, let us suppose that we have a function where y=2x+3 at x=3 and x=-2; this means we have both y-values [(3) and (-2)] plugged into our function, giving us 2×3+3 = 9 + 3 = 12 = 2×(-2) + 3 = -15 + 3 = -12 = 1/2 × (-2) × 2×(-1) – 1/(4).
How to Find the Inverse of a Function?
The inverse of a function is the function that is the inverse of another function. In other words, it is a mathematical operation that reverses the effect of the original function. For example, if f (x) = x2 + 1 and g(x) = f (x), then g(1) = 2 and g(3) = 4.
The inverse of a function f can be written as, where y=f(x). If you want to find its inverse, then you need to solve this equation for x by using the substitution method. This method involves substituting values in one variable with another variable and solving these equations.
Finding Inverse Function Using Algebra
You can find the inverse of a function by using the process of elimination, substitution, combination, and addition.
The process of elimination: This method helps you to find the inverse function. You need to use a table with two columns and one row. The first column has all the x values in ascending order like x=1,2,3… etc., whereas the second column has corresponding y values for those given x values like y = 3x+6 or 2y = 7x-5 etc., depending on which type of transformation is used by considering an equation with two variables as input and output respectively.
The process of substitution: This method also helps you to find out an inverse function but it involves substituting some arbitrary value in place of one variable such that its value changes into another variable’s value so that both (i) input data have become output data and (ii) output data remains unchanged when compared to input data which indicates that they are equal thus creating an identity between two equations with the same set of variables like Y=X+3 where Y represents output data whereas X represents input data.
Inverse Function Graph
The graph of an inverse function is the reflection of the graph of its original function about the y-axis. In other words, if you were to take a sheet of paper and draw two graphs on it, one for the original function and one for its inverse, then you could fold that paper over so that the two sheets touched at their common point (the x-axis) and make them into one. If you did this correctly, then both sides would be identical.
Inverse functions are always symmetric concerning their y-axis because any time you multiply a number by -1, it reverses direction: 2 becomes -2; 1 becomes -1; 4 becomes 3; etc. So, when we look at an inverse function’s graph from this new perspective—the side where all positive values have been replaced by negative ones—we see that they’re identical to each other!
Conclusion
In this blog, we have seen what is an inverse function with examples. In this blog, we have seen what is an inverse function with examples. We have also seen the properties of inverse functions.
