Question

What is the domain of the function below?

f(x) = log(x - 4) + 4

A: (-infinate, 4)
B: [4, infinate)
C: (-4, infinate)
D: (4, infinate)

Answer 1

The logarithm is defined only when its argument is (strictly) positive. So, you must impose

$x-4>0$

Just add 4 to both sides to get

$x > 4$

So, the domain is composed by all numbers greater than 4 (excluded), which is represented by the interval

$(4, \infty)$