A function has an inverse if passes both the vertical line test and horizontal line test .
The inverse of the function f is denoted by f⁻¹ and is pronounced "f inverse".
Although the inverse of a function looks like you're raising the function to the -1 power, it isn't. The inverse of a function does not mean the reciprocal of a function.
If the inverse of a function is also a function, then the inverse relation must pass a vertical line test. Since all the x-coordinates and y-coordinates are switched when finding the inverse, saying that the inverse must pass a vertical line test is the same as saying the original function must pass a horizontal line test.
If a function passes both the vertical line test (so that it is a function in the first place) and the horizontal line test (so that its inverse is a function), then the function is one-to-one and has an inverse function.
The graph of a function and its inverse are mirror images of each other. They are reflected about the identity function y=x.
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