Question

Find the domain of the following function.

f(x) = `sqrtlog(x^2 - 6x + 6)`

Answer 1

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, ∞).