Question

What is the domain of the function y = log(x + 3)?

Answer 1

The domain of the function y = log(x + 3) is all real numbers greater than -3, expressed as (-3, ∞) in interval notation.

Step-by-step explanation:

To determine the domain of the function y = log(x + 3), we need to consider the properties of the logarithmic function. Since the logarithm of a number is only defined for positive arguments, the expression inside the logarithm (x + 3) must be greater than zero.

We set up the inequality x + 3 > 0 and solve for x:

• x > -3

So, the domain of the function y = log(x + 3) is all real numbers greater than -3, which can be written in interval notation as (-3, ∞).

It's also useful to note the logarithmic property mentioned: The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. However, this isn't directly applicable to finding the domain.

Answer 2

Find the domain of

y = log(x + 3)

Logarithms can only be taken for positive numbers. So you must have

x + 3 > 0

x > – 3 ✔

So the domain of the function is

D = {x ∈ R: x > – 3}

or using the interval notation

D = (– 3, +∞)


I hope this helps. =)