When creating inverse functions, how do we know that these new functions are actually that? We can use the horizontal line test to see if an inverse of a function is also a function.
Horizontal Line Test
The inverse of a function is also a function if and only if every horizontal line drawn on the function only crosses the graph at no more than one point.
Use the horizontal test to see if the inverse of these function will also be a function.
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Notice that the graph of f(x) = x\(\small\mathsf{ ^2 }\) does not pass the horizontal line test. The horizontal lines cross the graph at more than one point.
On the other hand, f(x) = x does pass the horizontal line test. The horizontal lines only pass through the graph at one point.
