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

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

Given,fx=x12-x9+x4-x+1x12-x9+x4-x+1>0 since it lies inside rootx12+x4-x9-x+1>0x4x8+1-xx8+1+1>0x8+1x4-x+1>0now,x8+1 will be >0 for all xtaking x4-xfor x0 and x1x4xhence x4-x0hence x8+1x4-x+1>0 will be true for  x0 and x1for x0,1x4<xx4-x<0since 0< x<1x8<<<<<<1hence we can approximate  x8+1 to 1hence we have 1.x4-x+1>0since,-1< x4-x<0   x0,1hence domain of fx will be RxR

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