Question

Answer the following:

Find the domain of the following function.

f(x) = `sqrt(x - 3) + 1/(log(5 - x))`

Answer 1

f(x) = `sqrt(x - 3) + 1/(log(5 - x))`

For f to be defined,

x – 3 ≥ 0, 5 – x > 0 and 5 – x ≠ 1

∴ x ≥ 3, x < 5 and x ≠ 4

∴ Domian = [3, 4) ∪ (4, 5)