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Example 15 - f(x) = 1/x. What is the domain and range - Finding Domain and Range - By drawing graphs

  1. Chapter 2 Class 11 Relations and Functions
  2. Serial order wise
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Example 15 Define the real valued function f : R โ€“ {0} โ†’ R defined by f (x) = 1/๐‘ฅ xโˆˆ R โ€“ {0}. Complete the Table given below using this definition. What is the domain and range of this function? Given f(x) = 1/๐‘ฅ , x โˆˆ R โ€“ {0} We have to find f( โ€“ 2) To find f(-2), we put x = โ€“ 2 f(x) = 1/(โˆ’2) = โ€“ 0.5 To find f(-1.5), we put x = โ€“ 1.5 f(x) = 1/(โˆ’1.5) = โˆ’10/15 = โˆ’2/3 = โ€“ 0.66 To find f( โ€“ 1), we put x = โ€“ 1 f(x) = 1/(โˆ’1) = โˆ’1 To find f( โ€“ 0.5), we put x = โ€“ 0.5 f(x) = 1/(โˆ’0.5) = โˆ’10/5 = โ€“ 2 To find f(0.25), we put x = 0.25 f(x) = 1/0.25 = 100/25 = 4 To find f(0.5), we put x = 0.5 f(x) = 1/0.5 = 10/5 = 2 To find f(1), we put x = 1 f(x) = 1/1 = 1 To find f(1.5), we put x = 1.5 f(x) = 1/1.5 = 10/15 = 2/3 = 0.66 To find f(2), we put x = 2 f(x) = 1/2 = 0.5 Given f(x) = 1/๐‘ฅ , x โˆˆ R โ€“ {0} Hence, x & y can be any real number except 0 Domain = All possible values of x = R โ€“ {0} Range = All possible values of f(x) or y = R โ€“ {0}

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