Inverse tan domain and range | Trigonometry | Khan Academy

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I don't understand why we can't swap g(x) by x and, in the tan, swap x by g-1(x)

thelonearchitect
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0:39 How can or why did he switch the x and g(x) for g^-1(x)? It makes no sense to me because I probably missed a video

nacure
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At the end of the video, Sal asked what the range of inverse function of g(x) is. Is the range that Sal used arbitrary?

If so, can I say state any range restriction, as long as every x value outputs its own unique g^-1(x) value? E.g, (0, pi)?

bankaikun
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Imagine being the 10th comment on a video with nearly 150k views. Thanks for all the help (:

fanplate