Inverse of Functions

Let f(x) be defined as a function. If g(x) is the inverse, this means that f(g(x))=g(f(x))=x 

What does the inverse look like compared to the original function? The red curve is the original function and the yellow curve is the inverse.

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A function is also defined as a one to one mapping of an input to an output. What does this suggest about the nature of the inverse of functions?

What does the inverse of sin(x) look like?

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