Question

The domain of the relation R={(x,y):y=√xsquared-1}is​

A) x ≥ 1
B) x ≤ -1
C) x ∈ ℝ
D) x > 1

Answer 1

The domain of the relation R={(x,y):y=√xsquared-1} is x ≥ 1.

Step-by-step explanation:

The domain of the relation R={(x,y):y=√xsquared-1} is x ≥ 1.

To determine the domain, we need to find the values of x that are allowed in the relation. Since the expression √(x^2 - 1) represents the square root of a real number, the radicand must be greater than or equal to 0, to ensure the result is a real number.

Therefore, we have x^2 - 1 ≥ 0. Solving this inequality, we get (x - 1)(x + 1) ≥ 0. This means that either both factors are nonnegative, or both factors are negative.

So, x - 1 ≥ 0 and x + 1 ≥ 0, which leads to x ≥ 1.