find the domain and range of (x+7) /(x^2 - 8x + 4)

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Please find below the solution to the asked query:

fx=y=x+7x2-8x+4For fx to be defined, denominator must not be 0, hence,x2-8x+40x-42-16+40x-42-120x-4212x-4±23x4±23Hence domain is -,-4±23Nowy=x+7x2-8x+4yx2-8xy+4y=x+7yx2-x8y+1+4y-7=0As x is real, henceDiscriminant08y+12-4×y×4y-7064y2+1+16y-16y2+28y048y2+44y+10Factrize using Shridharacharya's formulay=-44±442-4×48×12×48=-44±174496=-44±410996=-11±10924=-11-10924 or -11+10924y--11-10924y--11+109240Hence range isy-11-10924 or y-11+10924

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