# Determining Inverse Functions and Relations

I've attached a problem set which contains the following questions related to inverse functions. Can you help explain the concepts to me?

Given point P of the function f(x), state the corresponding point P' in the inverse of the function.

Determine if the inverse of each relation graphed below is a function.

Find the inverse of each function.

Sketch the function and its inverse.

Describe the transformations that have taken place in the related graph of each function.

Graph the two relations and determine if the two relations are inverses.

https://brainmass.com/math/graphs-and-functions/determining-inverse-functions-relations-501095

## SOLUTION This solution is **FREE** courtesy of BrainMass!

It is possible to visualize the inverse of a function in terms of graphs if you consider that a function and its inverse mirror each other with the x = y line serving as the mirror of reflection. This analogy is particularly applicable in examples 6-8 where the question is asking for the inverse of a given point. In terms of finding the actual inverse of a given function one way is to replace the y with x in the initial function and then solve for y. For 9 through 11 and 19-24 keep in mind that a function is a one-to-one map from the domain of the x-axis to the range of the y-axis. In answering 25 and 26 keep in mind that it is also possible to reflect functions on a graph where the x-axis and the y-axis serve as mirrors although in these cases the resulting function is not the inverse it is just a translation or transformation. When graphing linear functions it is best to put the equation in the point-slope form y = mx + b where m= slope and b = y-intercept. When graphing quadratic equations it is best to refer to the standard format (for example the graph of x^2 + y^2 = r^2 is a circle with radius of r and centered at (0,0)).

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