Mark M. answered • 12/30/16

Mathematics Teacher - NCLB Highly Qualified

Mark M. answered • 12/30/16

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Mathematics Teacher - NCLB Highly Qualified

f(x) = x

A circle.

Stephen M. answered • 12/30/16

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Any of the equations from your previous question (function equals its inverse) would also answer the first part of your question. The key to a graph being a function is the vertical line test. If it also passes the horizontal line test, then it's inverse is also a function. So, f(x) = x is a function, and its inverse is also a function. You can easily verify this graphically. f(x) = x^{2} would be an example of a function whose inverse is a non-function, since the graph of a parabola passes the vertical line test but fails the horizontal line test. So, the second part of your question looks for a sketch of a curve that fails both the vertical and horizontal line tests. A circle would be a simple example, with equation x^{2} + y^{2} = 1. If you don't need the equation, you're welcome to sketch any wiggly curve you want that doubles back enough to fail both the vertical and horizontal line tests.^{}

If vertical/horizontal line tests still confuse you, you really ought to set up an online lesson with somebody so we can draw these examples on a whiteboard for you.

Kenneth S. answered • 12/30/16

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Give the equation of a function whose inverse is also a function. * y = x+1 is a function and because it's strictly increasing it passes the HORIZONTAL LINE TEST and therefore it has an inverse.*

sketch a non-function whose inverse is also a non-function.

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