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Question
Find the domain of f(x) = log10 (x2 − 5x + 6)
Solution
f(x) = log10 (x2 − 5x + 6)
f(x) is defined only if x2 − 5x + 6 > 0
i.e., if x2 − 5x > − 6
i.e., if `x^2 - 5x + 25/4 > - 6 + 25/4`
i.e., if `(x - 5/2)^2 > 1/4`
i.e., if `x - 5/2 > 1/2` or `x - 5/2 < - 1/2`
i.e. If x > 3 or x < 2
∴ f(x) is defined if x < 2 or x > 3
∴ Domain = `( - ∞, 2) ∪ (3, ∞)`
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