What is the domain of f(x) = log₂(x + 3) + 2?

Solution:

The domain of the function given in the problem statement implies the value which the variable x can take:

For f(x) to be defined (x + 3) > 0

x > -3

Therefore the domain of function f(x) is (-3, ∞), {x/ x > -3}

Another function for which the domain can be ascertained is: f(x) = log(x +3)/(x² + 3x + 2)

For f(x) to be defined (x + 3) > 0

Which implies x > -3

Also x² + 3x + 2 = (x + 1)(x + 2)

And again for f(x) to be defined (x + 1)(x + 2) ≠ 0

Which implies x ≠ -domain of he 1 and x ≠ -2,

Therefore the function f(x) is {-3, ∞} - {-1, -2}

What is the domain of f(x) = log2(x + 3) + 2?

Summary:

The domain of f(x) = log2(x + 3) + 2 is (-3, ∞}, {x/ x > -3}