Misc 3 - Find domain of f(x) = x2 + 2x + 1 / x2 - 8x + 12 - Finding Domain and Range - General Method

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Misc 3 Find the domain of the function "f" (x) = (" " ๐‘ฅ2 +2๐‘ฅ +1)/(๐‘ฅ2 โˆ’8๐‘ฅ+12) "f" (x) = (" " x2 +2x +1)/(x2 โˆ’8x+12) = (" " (x +1)2)/(x2 โˆ’2x โˆ’6๐‘ฅ +12) = ((x +1)2)/(๐‘ฅ(x โˆ’2) โˆ’6(๐‘ฅ โˆ’2)) = (" " (x +1)2)/((๐‘ฅ โˆ’ 6)(x โˆ’2) ) In real numbers , the denominator cannot be zero Hence (x โ€“ 6) (x โ€“ 2) โ‰  0 โ‡’ x โ‰  6 and x โ‰  2 Hence the domain of the function will be all real numbers except 2 and 6 Hence, the domain = R โ€“ {2, 6},

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