Find the domain of the following functions. fx = √x-3 + 1/log(5-x)

Question

Find the domain of the following functions.

f(x) = \(\sqrt {x-3}+ \frac{1}{log (5-x)}\)

fx = √x-3 + 1/log(5-x)

Answer 1

f(x) = \(\sqrt{x-3} + \frac {1}{log(5-x)}\)

For f to be defined,

x – 3 ≥ 0, 5 – x > 0 and 5 – x ≠ 1 

x ≥ 3, x < 5 and x ≠ 4 

∴ Domain of f = [3, 4) ∪ (4, 5)