1. Chapter 2 Class 11 Relations and Functions
2. Serial order wise
3. Examples

Transcript

Example 15 Define the real valued function f : R โ {0} โ R defined by f (x) = 1/๐ฅ xโ 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 โ R โ {0} We have to find f( โ 2) To find f(-2), we put x = โ 2 f(x) = 1/(โ2) = โ 0.5 To find f(-1.5), we put x = โ 1.5 f(x) = 1/(โ1.5) = โ10/15 = โ2/3 = โ 0.66 To find f( โ 1), we put x = โ 1 f(x) = 1/(โ1) = โ1 To find f( โ 0.5), we put x = โ 0.5 f(x) = 1/(โ0.5) = โ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 โ 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}

Examples