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Question
Find the domain of the following function.
f(x) = `sqrtlog(x^2 - 6x + 6)`
Solution
f(x) = `sqrtlog(x^2 - 6x + 6)`
is defined when
log(x2 − 6x + 6) ≥ 0
log(x2 − 6x + 6) ≥ 1 ⇒ (x - 5)(x - 1) ≥ 0
This inequality holds if x ≤ 1 or x ≥ 5. Hence, the domain of the function is (−∞, 1) ∪(5, ∞).
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