Last updated at Jan. 28, 2020 by
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Example 15 Define the real valued function f : R β {0} β R defined by f (x) = 1/π₯ x β R β {0}. Complete the Table given below using this definition. What is the domain and range of this function? Given f(x) = 1/π₯ , x β R β {0} Finding f(x) at different values of x f(β2) = 1/(β2) = β 0.5 f(β1.5) = 1/(β1.5) = β10/15 = β2/3 = β 0.66 f(β1) = 1/(β1) = β1 f(β0.5) = 1/(β0.5) = β10/5 = β 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 β R β {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 β {0} Range = All possible values of f(x) or y = R β {0}
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