Question

Find the domain of f(x) = log₁₀ (x² − 5x + 6)

Answer 1

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, ∞)`