Learn All Concepts of Chapter 2 Class 11 Relations and Function - FREE. Check - Relation and Function Class 11 - All Concepts

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  1. Chapter 2 Class 11 Relations and Functions
  2. Concept wise

Transcript

Example 15 Define the real valued function f : R โ€“ {0} โ†’ R defined by f (x) = 1/๐‘ฅ x โˆˆ 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} Finding f(x) at different values of x f(โˆ’2) = 1/(โˆ’2) = โ€“ 0.5 f(โˆ’1.5) = 1/(โˆ’1.5) = โˆ’10/15 = โˆ’2/3 = โ€“ 0.66 f(โˆ’1) = 1/(โˆ’1) = โˆ’1 f(โˆ’0.5) = 1/(โˆ’0.5) = โˆ’10/5 = โ€“ 2 f(0.25) = 1/0.25 = 100/25 = 4 f(0.5) = 1/0.5 = 10/5 = 2 f(1) = 1/1 = 1 f(1.5) = 1/1.5 = 10/15 = 2/3 = 0.66 f(2) = 1/2 = 0.5 So, our table looks like Domain and Range Given f(x) = 1/๐‘ฅ , x โˆˆ R โ€“ {0} For x = 0, y = 1/0 = Not Defined For y = 0, x = 1/0 = Not Defined 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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