Question

If you have a function and it’s inverse, how can you be sure that both equations represent functions?

Answer 1

Answer:

When you plot the graph of either, it passes both the horizontal and vertical line tests.

Step-by-step explanation:

A function will pass the vertical line test. This is what make a relation a function. It will have an inverse function if it also passes the horizontal line test. (The inverse function is the reflection of the function across the line y=x.)

Of course, the domain of one is the range of the other, and vice versa.

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The vertical line test passes if no vertical line intersects the graph of the relation in more than one point. The horizontal line test is similar: no horizontal line can intersect the graph in more than one point.