Consider the function f(x) = (√5x − 5) + 1. Which inequality is used to find the domain?

The mathematical expressions in which both sides may or may not be equal are called inequalities. In inequality, unlike equations, we compare two values. The equal sign in between is replaced by less than, greater than, or not equal to sign.

Answer: For the function f(x) = (√5x − 5) + 1, the domain is Df(x) ∈ [1,∞). Greater than equal to inequality is used to find the domain of the given function.

Let's look into the solution step by step to find the domain.

Explanation:

Given: f(x) = (√5x − 5) + 1.

To find the domain, let's look into the term inside the square root.

We know that for f(x) to be real, 5x - 5 should be a positive number as we cannot have a square root of a negative number for a real-valued function.

Thus,

5x - 5 ≥ 0

⇒ 5x ≥ 5

⇒ x ≥ 1

Thus, x can be any value ranging from 1 to infinity.

Thus, for the function f(x) = (√5x − 5) + 1, the domain is Df(x) ∈ [1,∞). We used greater than equal to inequality to find the domain.