find the domain of these functions.please explain them briefly.

Dear Student,
Please find below the solution to the asked query:

Given,fx=sin-13-2x5+3-xvalue inside root can be 03-x0x3for sin-1x, to exist -1x1-13-2x513-2x513-2x52x-2x-1-13-2x5-53-2x2x8x4we have inequality,x3x-1x4taking interseection we getDomain=x-1,3

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