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Example 15 - f(x) = 1/x. What is the domain and range - Examples

Example 15 - Chapter 2 Class 11 Relations and Functions - Part 2
Example 15 - Chapter 2 Class 11 Relations and Functions - Part 3 Example 15 - Chapter 2 Class 11 Relations and Functions - Part 4

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Example 15 Define the real valued function f : R – {0} β†’ R defined by f (x) = 1/π‘₯ x ∈ R – {0}. Complete the Table given below using this definition. What is the domain and range of this function? Given f(x) = 1/π‘₯ , x ∈ R – {0} Finding f(x) at different values of x f(βˆ’2) = 1/(βˆ’2) = – 0.5 f(βˆ’1.5) = 1/(βˆ’1.5) = βˆ’10/15 = βˆ’2/3 = – 0.66 f(βˆ’1) = 1/(βˆ’1) = βˆ’1 f(βˆ’0.5) = 1/(βˆ’0.5) = βˆ’10/5 = – 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/π‘₯ , x ∈ R – {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 – {0} Range = All possible values of f(x) or y = R – {0}

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