Consider the function f(x) = (√5x − 5) + 1. Which inequality is used to find the domain?
The mathematical expressions in which both sides are not equal are called inequalities. In inequality, unlike in equations, we compare two values. The equal to 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,∞).
Let's look into the solution step by step to find the domain.
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.
5x - 5 ≥ 0
⇒ 5x ≥ 5
⇒ x ≥ 1
Thus, x can be any value ranging from 1 to infinity.