Example 21 - Find domain of f(x) = x2 + 3x + 5 / x2 - 5x + 4 - Examples

  1. Chapter 2 Class 11 Relations and Functions
  2. Serial order wise
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Example 21 Find the domain of the function "f" (x) = (" " ๐‘ฅ2 + 3๐‘ฅ + 5)/(๐‘ฅ2 โˆ’ 5๐‘ฅ + 4) "f" (x) = (" " x2 + 3x + 5)/(x2 โˆ’ 5x + 4) = (x2 + 3x + 5)/(x2 โˆ’ 4x โˆ’ ๐‘ฅ + 4) = (x2 + 3x +5)/(๐‘ฅ(x โˆ’ 4) โˆ’1(๐‘ฅ โˆ’ 4)) = (x2 + 3x + 5)/((๐‘ฅ โˆ’ 4)(x โˆ’1) ) In real numbers , the denominator cannot be zero Hence (x โ€“ 4) (x โ€“ 1) โ‰  0 โ‡’ x โ‰  4 and x โ‰  1 Hence the domain of the function will be all real numbers except 1 and 4 Hence, the domain = R โ€“ {1, 4}.

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