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Last updated at Jan. 28, 2020 by Teachoo
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Example 15 Define the real valued function f : R โ {0} โ R defined by f (x) = 1/๐ฅ x โ R โ {0}. Complete the Table given below using this definition. What is the domain and range of this function? Given f(x) = 1/๐ฅ , x โ R โ {0} Finding f(x) at different values of x f(โ2) = 1/(โ2) = โ 0.5 f(โ1.5) = 1/(โ1.5) = โ10/15 = โ2/3 = โ 0.66 f(โ1) = 1/(โ1) = โ1 f(โ0.5) = 1/(โ0.5) = โ10/5 = 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) = 1/๐ฅ , x โ 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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