find the range of √(2-x) + √(1+x)

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Please find below the solution to the asked query:

fx=2-x+1+xQuantity inside root must be positive2-x0 and 1+x0x2 and x-1Take common valuesHence domain is x-1,2f-1=2+1+0=3f2=0+1+2=3Differentiate fx with respect to xf'x=-122-x+121+xFor maxima/mnima, f'x=0121+x=122-x2-x=1+x2x=3x=32Hencef32=2-32+1+32=12+52=62=32Hence domain is 3,32

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