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Question
Find the domain and range of the following function.
g(x) = `(x + 4)/(x - 2)`
Solution
g(x) = `(x + 4)/(x - 2)`
g(x) is not defined only for x = 2
∴ Domain = {x/x ∈ R, x ≠ 2} = R – {2}
Let y = `(x + 4)/(x - 2)`
∴ xy – 2y = x + 4
∴ xy – x = 2y + 4
∴ x(y – 1) = 2y + 4
∴ x = `(2y + 4)/(y - 1)`
If y = 1, we cannot find x such that g(x) = 1
∴ Range = {y/y ∈ R, y ≠ 1} = R – {1}
∴ Domain = {x/x ∈ R, x ≠ 2} = R – {2}
Range = {y/y ∈ R, y ≠ 1} = R – {1}
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